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    <link:label id="lab_kai_BankersAcceptanceDraftsFairValueDisclosure_b1d8f8e5-1923-40b0-8077-fae9fadae1a7_terseLabel_en-US" xlink:label="lab_kai_BankersAcceptanceDraftsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Banker's acceptance drafts</link:label>
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    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferredLiabilitiesIncurred_3d4b68f7-4bd0-42a2-aba7-5b46ee806d7a_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferredLiabilitiesIncurred" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Post closing adjustments</link:label>
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    <link:label id="lab_us-gaap_IncomeTaxReconciliationTaxCreditsResearch_08042f6c-6da2-4fbf-82d7-67fb576c1fcf_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationTaxCreditsResearch" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Research and development tax credits</link:label>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationTaxCreditsResearch_label_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationTaxCreditsResearch" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Tax Credit, Research, Amount</link:label>
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    <link:label id="lab_us-gaap_GoodwillLineItems_e4203bd3-970a-4e2e-9200-89503184cf32_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill [Line Items]</link:label>
    <link:label id="lab_us-gaap_GoodwillLineItems_label_en-US" xlink:label="lab_us-gaap_GoodwillLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillLineItems" xlink:to="lab_us-gaap_GoodwillLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByMeasurementBasisAxis_35f59752-1e4b-4b49-ab1d-046ec2c0916b_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Basis [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByMeasurementBasisAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Basis [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByMeasurementBasisAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByMeasurementBasisAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByMeasurementBasisAxis" xlink:to="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAxis_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation:</link:label>
    <link:label id="lab_ecd_AdjToCompAxis_label_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AdjToCompAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAxis" xlink:to="lab_ecd_AdjToCompAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NamedExecutiveOfficersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Named Executive Officers, Footnote</link:label>
    <link:label id="lab_ecd_NamedExecutiveOfficersFnTextBlock_label_en-US" xlink:label="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Named Executive Officers, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NamedExecutiveOfficersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NamedExecutiveOfficersFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NamedExecutiveOfficersFnTextBlock" xlink:to="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferredAbstract_343bf381-95c8-4dd1-b9c8-269ac353ae9f_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferredAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchase Price:</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferredAbstract_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferredAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationConsiderationTransferredAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationConsiderationTransferredAbstract"/>
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    <link:label id="lab_kai_KeyKnifeIncMember_293dec26-d39a-495b-a6fb-64f86b0d31a3_terseLabel_en-US" xlink:label="lab_kai_KeyKnifeIncMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Key Knife, Inc.</link:label>
    <link:label id="lab_kai_KeyKnifeIncMember_label_en-US" xlink:label="lab_kai_KeyKnifeIncMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Key Knife, Inc. [Member]</link:label>
    <link:label id="lab_kai_KeyKnifeIncMember_documentation_en-US" xlink:label="lab_kai_KeyKnifeIncMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Key Knife, Inc.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_KeyKnifeIncMember" xlink:href="kai-20260103.xsd#kai_KeyKnifeIncMember"/>
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    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesEmployeeStockPurchasePlans_39975c61-e851-4428-b2df-b92abeea5c0f_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesEmployeeStockPurchasePlans" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock issued during period under ESOP (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesEmployeeStockPurchasePlans_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesEmployeeStockPurchasePlans" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Employee Stock Purchase Plans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesEmployeeStockPurchasePlans" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodSharesEmployeeStockPurchasePlans"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesEmployeeStockPurchasePlans" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesEmployeeStockPurchasePlans" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DueFromCustomerAcceptances_ab98be37-da6c-45d1-9c45-0817a25cc801_terseLabel_en-US" xlink:label="lab_us-gaap_DueFromCustomerAcceptances" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due from bankers acceptances drafts</link:label>
    <link:label id="lab_us-gaap_DueFromCustomerAcceptances_label_en-US" xlink:label="lab_us-gaap_DueFromCustomerAcceptances" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Due from Customer Acceptances</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DueFromCustomerAcceptances" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DueFromCustomerAcceptances"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DueFromCustomerAcceptances" xlink:to="lab_us-gaap_DueFromCustomerAcceptances" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock_0a4f73f0-eaea-4bfa-8fd4-e906a622892c_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reconciliation of cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Cash and Cash Equivalents [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CurrentIncomeTaxExpenseBenefit_694bbdc0-2117-4edf-96e2-e5030e12936d_totalLabel_en-US" xlink:label="lab_us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Current provision</link:label>
    <link:label id="lab_us-gaap_CurrentIncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CurrentIncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation, Amount</link:label>
    <link:label id="lab_ecd_AdjToCompAmt_label_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AdjToCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAmt" xlink:to="lab_ecd_AdjToCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligationPercentage_76181bce-c71b-47c4-a9a6-a199c441b81a_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligationPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue, remaining performance obligation, percent</link:label>
    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligationPercentage_label_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligationPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue, Remaining Performance Obligation, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueRemainingPerformanceObligationPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenueRemainingPerformanceObligationPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueRemainingPerformanceObligationPercentage" xlink:to="lab_us-gaap_RevenueRemainingPerformanceObligationPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets_0e835d8c-76ff-4b85-a5cb-607ecf10470f_negatedLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Operating Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInOtherOperatingAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_97091226-7380-4bdd-9706-1ed5b3a1d21c_terseLabel_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Principles of Consolidation</link:label>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConsolidationPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:to="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensation_50a62025-e3ec-4b13-a876-4125268f8a71_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock-based compensation expense</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Noncash Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensation" xlink:to="lab_us-gaap_ShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_RestructuringIncurredCostStatementOfIncomeOrComprehensiveIncomeExtensibleEnumerationNotDisclosedFlag_019b8298-ac3a-70b8-8fed-a44b55477817_terseLabel_en-US" xlink:label="lab_kai_RestructuringIncurredCostStatementOfIncomeOrComprehensiveIncomeExtensibleEnumerationNotDisclosedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restructuring Incurred Cost Statement Of Income Or Comprehensive Income Extensible Enumeration Not Disclosed Flag</link:label>
    <link:label id="lab_kai_RestructuringIncurredCostStatementOfIncomeOrComprehensiveIncomeExtensibleEnumerationNotDisclosedFlag_label_en-US" xlink:label="lab_kai_RestructuringIncurredCostStatementOfIncomeOrComprehensiveIncomeExtensibleEnumerationNotDisclosedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restructuring Incurred Cost Statement Of Income Or Comprehensive Income Extensible Enumeration Not Disclosed Flag</link:label>
    <link:label id="lab_kai_RestructuringIncurredCostStatementOfIncomeOrComprehensiveIncomeExtensibleEnumerationNotDisclosedFlag_documentation_en-US" xlink:label="lab_kai_RestructuringIncurredCostStatementOfIncomeOrComprehensiveIncomeExtensibleEnumerationNotDisclosedFlag" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Restructuring Incurred Cost Statement Of Income Or Comprehensive Income Extensible Enumeration Not Disclosed Flag</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_RestructuringIncurredCostStatementOfIncomeOrComprehensiveIncomeExtensibleEnumerationNotDisclosedFlag" xlink:href="kai-20260103.xsd#kai_RestructuringIncurredCostStatementOfIncomeOrComprehensiveIncomeExtensibleEnumerationNotDisclosedFlag"/>
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    <link:label id="lab_kai_BusinessAcquisitionRevenueAndEarningsLossOfAcquireeSinceAcquisitionDateTableTextBlock_5cf5835a-e11c-4d61-8c70-83cb276158a6_terseLabel_en-US" xlink:label="lab_kai_BusinessAcquisitionRevenueAndEarningsLossOfAcquireeSinceAcquisitionDateTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue and Operating Income</link:label>
    <link:label id="lab_kai_BusinessAcquisitionRevenueAndEarningsLossOfAcquireeSinceAcquisitionDateTableTextBlock_label_en-US" xlink:label="lab_kai_BusinessAcquisitionRevenueAndEarningsLossOfAcquireeSinceAcquisitionDateTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Acquisition, Revenue And Earnings (Loss) Of Acquiree Since Acquisition Date [Table Text Block]</link:label>
    <link:label id="lab_kai_BusinessAcquisitionRevenueAndEarningsLossOfAcquireeSinceAcquisitionDateTableTextBlock_documentation_en-US" xlink:label="lab_kai_BusinessAcquisitionRevenueAndEarningsLossOfAcquireeSinceAcquisitionDateTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Acquisition, Revenue And Earnings (Loss) Of Acquiree Since Acquisition Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_BusinessAcquisitionRevenueAndEarningsLossOfAcquireeSinceAcquisitionDateTableTextBlock" xlink:href="kai-20260103.xsd#kai_BusinessAcquisitionRevenueAndEarningsLossOfAcquireeSinceAcquisitionDateTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_BusinessAcquisitionRevenueAndEarningsLossOfAcquireeSinceAcquisitionDateTableTextBlock" xlink:to="lab_kai_BusinessAcquisitionRevenueAndEarningsLossOfAcquireeSinceAcquisitionDateTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Employee Stock Option</link:label>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_label_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Option [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockOptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EmployeeStockOptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeStockOptionMember" xlink:to="lab_us-gaap_EmployeeStockOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_5ad14b64-7688-4b9c-b0be-db81f22f8b3a_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfPropertyPlantAndEquipmentTable"/>
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    <link:label id="lab_kai_EmployeeStockOwnershipPlanEsopDiscountToMarket_c64afbb3-c8d8-4d8a-9a78-f9b46f47edce_terseLabel_en-US" xlink:label="lab_kai_EmployeeStockOwnershipPlanEsopDiscountToMarket" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discount to market under the ESOP</link:label>
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    <link:label id="lab_us-gaap_FinanceLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList_0c020af2-3ed9-404c-b148-46c6f1920109_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, Noncurrent, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, Noncurrent, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList"/>
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    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperationsTaxRateReconciliationAbstract_019bb2ab-b494-7363-bdb2-b6880861551e_verboseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperationsTaxRateReconciliationAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Percent</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateContinuingOperationsTaxRateReconciliationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateContinuingOperationsTaxRateReconciliationAbstract"/>
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    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_1da61c23-7f7a-40cd-a55e-87c8ab8f3354_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities [Axis]</link:label>
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    <link:label id="lab_us-gaap_AssetImpairmentCharges_463ff342-1924-4feb-a3a2-1ca0172a64f4_terseLabel_en-US" xlink:label="lab_us-gaap_AssetImpairmentCharges" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Impairment loss</link:label>
    <link:label id="lab_us-gaap_AssetImpairmentCharges_label_en-US" xlink:label="lab_us-gaap_AssetImpairmentCharges" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Impairment Charges</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetImpairmentCharges" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetImpairmentCharges"/>
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    <link:label id="lab_us-gaap_StockholdersEquity_72b48fa0-af03-462e-8dbd-f3a8b20602fc_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Kadant Stockholders' Equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_label_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquity" xlink:to="lab_us-gaap_StockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingPoliciesProcLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures [Line Items]</link:label>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTextBlock_c8f1b326-9a19-4bbd-a632-f802390cb645_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, plant and equipment</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTextBlock_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_51d68881-e6a6-4712-9e64-ac53fc66579d_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesAuthorized" xlink:to="lab_us-gaap_CommonStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_aba0e0a6-20db-4826-9781-7d99ca94e4fa_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities and Stockholders' Equity</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAndStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StateAndLocalJurisdictionMember_43feff28-5448-4ac1-86b6-5e0d9d8a12d0_terseLabel_en-US" xlink:label="lab_us-gaap_StateAndLocalJurisdictionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">State and local jurisdiction</link:label>
    <link:label id="lab_us-gaap_StateAndLocalJurisdictionMember_label_en-US" xlink:label="lab_us-gaap_StateAndLocalJurisdictionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">State and Local Jurisdiction [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StateAndLocalJurisdictionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StateAndLocalJurisdictionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StateAndLocalJurisdictionMember" xlink:to="lab_us-gaap_StateAndLocalJurisdictionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CoverAbstract_8f03b325-2154-42be-9b8b-7209faff41a1_terseLabel_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cover [Abstract]</link:label>
    <link:label id="lab_dei_CoverAbstract_label_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cover [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CoverAbstract" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CoverAbstract"/>
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    <link:label id="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure_fa085b4a-2727-48b9-b0ac-b1e6aa5c70f4_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Money market funds and time deposits</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAndCashEquivalentsFairValueDisclosure"/>
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    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_88e8f82c-079e-4178-bbca-9949d6152b8f_terseLabel_en-US" xlink:label="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Portion at Fair Value Measurement</link:label>
    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Portion at Fair Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PortionAtFairValueFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:to="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MaximumMember_fd7f4133-a42a-470a-a4eb-085ca1fedf95_terseLabel_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum</link:label>
    <link:label id="lab_srt_MaximumMember_label_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maximum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MaximumMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MaximumMember"/>
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    <link:label id="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_af1c864a-db20-4653-8a01-7cd594978e87_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net Income Attributable to Noncontrolling Interests</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLossAttributableToNoncontrollingInterest"/>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeDefinedBenefitPlansNetUnamortizedGainLossArisingDuringPeriodTax_21f3ae20-014f-42cb-a930-b999c568a816_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeDefinedBenefitPlansNetUnamortizedGainLossArisingDuringPeriodTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension and other post-retirement liability adjustments, net, tax</link:label>
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    <link:label id="lab_us-gaap_FairValueAdjustmentToInventoryMember_cb0a52a5-27a1-4312-802a-6ec3f6a41748_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAdjustmentToInventoryMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Inventory revalued</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:to="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_TradingSymbol_be94e470-34a7-476a-89fb-2c8cc72a8cbc_terseLabel_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:label id="lab_dei_TradingSymbol_label_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_TradingSymbol"/>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_a9e396e1-0559-4943-adc1-dfb5c6e2cd82_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour"/>
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    <link:label id="lab_us-gaap_BusinessCombinationsPolicy_81a8baca-8b15-430d-a55e-b82447be0888_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationsPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combinations</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationsPolicy_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationsPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationsPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationsPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationsPolicy" xlink:to="lab_us-gaap_BusinessCombinationsPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance_019c56c2-0ddb-7e46-af9e-fe91c97157f9_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changes in Valuation Allowances</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Change in Deferred Tax Assets Valuation Allowance, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance"/>
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    <link:label id="lab_us-gaap_OperatingLossCarryforwardsTable_4e429c7a-d76d-4390-a2d9-321668b48abd_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLossCarryforwardsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Loss Carryforwards [Table]</link:label>
    <link:label id="lab_us-gaap_OperatingLossCarryforwardsTable_label_en-US" xlink:label="lab_us-gaap_OperatingLossCarryforwardsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Loss Carryforwards [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLossCarryforwardsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLossCarryforwardsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLossCarryforwardsTable" xlink:to="lab_us-gaap_OperatingLossCarryforwardsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_b1fee622-5f86-481e-a9f0-b75a867c9458_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Activity under stock plans (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Shares Issued, Shares, Share-Based Payment Arrangement, after Forfeiture</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation"/>
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    <link:label id="lab_dei_EntityAddressCityOrTown_e22f8165-8c90-4676-93fb-d446fc7854b8_terseLabel_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:label id="lab_dei_EntityAddressCityOrTown_label_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressCityOrTown"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressCityOrTown" xlink:to="lab_dei_EntityAddressCityOrTown" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_A2025AcquisitionMember_019b8229-22d3-7e04-9b75-ad5edd6af605_terseLabel_en-US" xlink:label="lab_kai_A2025AcquisitionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2025 Acquisition</link:label>
    <link:label id="lab_kai_A2025AcquisitionMember_label_en-US" xlink:label="lab_kai_A2025AcquisitionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2025 Acquisition [Member]</link:label>
    <link:label id="lab_kai_A2025AcquisitionMember_documentation_en-US" xlink:label="lab_kai_A2025AcquisitionMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2025 Acquisition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_A2025AcquisitionMember" xlink:href="kai-20260103.xsd#kai_A2025AcquisitionMember"/>
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    <link:label id="lab_us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent_bb3214a2-d3d5-467d-9ed4-66d6ba3ff637_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance lease, weighted average discount rate (percent)</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Weighted Average Discount Rate, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent"/>
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    <link:label id="lab_kai_CapitalMember_8b963b84-45cf-40b2-a49f-45975c96c90e_terseLabel_en-US" xlink:label="lab_kai_CapitalMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital</link:label>
    <link:label id="lab_kai_CapitalMember_label_en-US" xlink:label="lab_kai_CapitalMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Capital [Member]</link:label>
    <link:label id="lab_kai_CapitalMember_documentation_en-US" xlink:label="lab_kai_CapitalMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Capital [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_CapitalMember" xlink:href="kai-20260103.xsd#kai_CapitalMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_CapitalMember" xlink:to="lab_kai_CapitalMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_8b834afb-eec5-4218-8acd-788343b552f5_terseLabel_en-US" xlink:label="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exchange Rate Effect on Cash, Cash Equivalents, and Restricted Cash</link:label>
    <link:label id="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_label_en-US" xlink:label="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effect of Exchange Rate on Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Continuing Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents"/>
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    <link:label id="lab_us-gaap_DeferredTaxAssetsNet_d52df8c9-88c3-4379-9aec-9fe390a01c48_totalLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Deferred tax asset, net</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsNet_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Net of Valuation Allowance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsNet" xlink:to="lab_us-gaap_DeferredTaxAssetsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonPeoNeoAvgCompActuallyPaidAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:to="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedStockUnitsRSUMember_311aaa1d-15d9-4641-8ce6-50eba4e69503_verboseLabel_en-US" xlink:label="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Restricted stock unit awards</link:label>
    <link:label id="lab_us-gaap_RestrictedStockUnitsRSUMember_bf081bdc-59e4-4688-8f85-1ff9675ce31f_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">RSU Awards</link:label>
    <link:label id="lab_us-gaap_RestrictedStockUnitsRSUMember_label_en-US" xlink:label="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Stock Units (RSUs) [Member]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedStockUnitsRSUMember" xlink:to="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementLocationDomain_6b36cd61-01cc-4558-ad57-3f56f09a1f66_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Income Location, Balance [Domain]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementLocationDomain_label_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Income Location, Balance [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementLocationDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementLocationDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementLocationDomain" xlink:to="lab_us-gaap_IncomeStatementLocationDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherInventoryInventoryAtOffSitePremises_3ab84013-29da-4d03-a80f-ce997c9e4c28_terseLabel_en-US" xlink:label="lab_us-gaap_OtherInventoryInventoryAtOffSitePremises" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finished goods, at customer locations</link:label>
    <link:label id="lab_us-gaap_OtherInventoryInventoryAtOffSitePremises_label_en-US" xlink:label="lab_us-gaap_OtherInventoryInventoryAtOffSitePremises" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Inventory, Inventory at off Site Premises, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherInventoryInventoryAtOffSitePremises" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherInventoryInventoryAtOffSitePremises"/>
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    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CompActuallyPaidVsOtherMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferred1_c7de7bbf-24eb-4326-9c89-defa1a76b723_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consideration transferred</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferred1_4aaeee1c-9369-4dba-ac04-14797ec85ba2_totalLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Consideration transferred</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferred1_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred</link:label>
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    <link:label id="lab_us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1_486714fa-ce91-4f9b-99b4-488df83a3ff9_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance lease, weighted average remaining lease term (years)</link:label>
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    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year</link:label>
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    <link:label id="lab_us-gaap_DeferredFinanceCostsNet_019b8243-c105-78e1-908f-20e0fd5f7995_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt issuance costs, net</link:label>
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    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill_ce9b3b99-6bd5-4823-ab68-60c9a67a15b7_verboseLabel_en-US" xlink:label="lab_us-gaap_IndefiniteLivedIntangibleAssetsExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net</link:label>
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    <link:label id="lab_us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount_b3a740d1-9ee2-40b4-87f5-d021a82e7af3_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Less: Imputed Interest</link:label>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber_d6a5600e-91ac-4570-8ee5-f89efdec0637_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unvested RSUs (in shares)</link:label>
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    <link:label id="lab_us-gaap_StandardProductWarrantyPolicy_2f9eb9d4-a2bb-4117-83fd-8159c87c1963_terseLabel_en-US" xlink:label="lab_us-gaap_StandardProductWarrantyPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warranty Obligations</link:label>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_e2fa8cbe-5483-4f11-985e-aeb1982f8ff1_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by operating activities</link:label>
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    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsOther_6b2e1a10-651a-4ba9-b7a4-0900e04daf7f_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsOther" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Current Assets</link:label>
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    <link:label id="lab_us-gaap_Depreciation_f8abadae-1a06-41d2-9def-4175a894de12_terseLabel_en-US" xlink:label="lab_us-gaap_Depreciation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation expense</link:label>
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    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_7dc67e2d-88c7-4ac5-98f2-e632da37b1f0_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term Debt, Type [Axis]</link:label>
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    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour_9dd67300-3c8e-48cc-b587-e1b7d695d618_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentLineItems_94ca29af-6b6a-4405-8610-36eb16fe6390_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment [Line Items]</link:label>
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    <link:label id="lab_us-gaap_StandardProductWarrantyAccrualAdditionsFromBusinessAcquisition_e20a0470-c76d-4dad-9e11-d6c97a576b9f_terseLabel_en-US" xlink:label="lab_us-gaap_StandardProductWarrantyAccrualAdditionsFromBusinessAcquisition" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquisitions</link:label>
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    <link:label id="lab_kai_BusinessCombinationConsiderationTransferredContingentConsiderationFairValueDisclosure_documentation_en-US" xlink:label="lab_kai_BusinessCombinationConsiderationTransferredContingentConsiderationFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Contingent Consideration, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_BusinessCombinationConsiderationTransferredContingentConsiderationFairValueDisclosure" xlink:href="kai-20260103.xsd#kai_BusinessCombinationConsiderationTransferredContingentConsiderationFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_BusinessCombinationConsiderationTransferredContingentConsiderationFairValueDisclosure" xlink:to="lab_kai_BusinessCombinationConsiderationTransferredContingentConsiderationFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressStateOrProvince_608f86f5-cf35-4e9f-b9cc-c70ab1ddd782_terseLabel_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:label id="lab_dei_EntityAddressStateOrProvince_label_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
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    <link:label id="lab_us-gaap_FinanceLeasePrincipalPayments_cb3488f2-dab8-496d-a98e-b21e298b5fd6_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeasePrincipalPayments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing cash flows from finance leases</link:label>
    <link:label id="lab_us-gaap_FinanceLeasePrincipalPayments_label_en-US" xlink:label="lab_us-gaap_FinanceLeasePrincipalPayments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Principal Payments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeasePrincipalPayments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeasePrincipalPayments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeasePrincipalPayments" xlink:to="lab_us-gaap_FinanceLeasePrincipalPayments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_03e48cf1-c496-465c-906d-11d6b62d7f3c_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Security, Excluded EPS Calculation [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Security, Excluded EPS Calculation [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable"/>
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    <link:label id="lab_us-gaap_LiabilitiesCurrent_b947f254-1c81-4a7c-9a19-87e87ea4bbd5_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Current Liabilities</link:label>
    <link:label id="lab_us-gaap_LiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesCurrent" xlink:to="lab_us-gaap_LiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsInventory_32c45cf3-d767-4ff7-b2f4-908f14772d22_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsInventory" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Inventory basis difference</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsInventory_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsInventory" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Inventory</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsInventory" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsInventory"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsInventory" xlink:to="lab_us-gaap_DeferredTaxAssetsInventory" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_IndividualAxis_terseLabel_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Individual:</link:label>
    <link:label id="lab_ecd_IndividualAxis_label_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Individual [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_IndividualAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_IndividualAxis"/>
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    <link:label id="lab_us-gaap_DefinedContributionPlanCostRecognized_fc9170cd-a68a-4057-880f-a6d410dbc0d3_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedContributionPlanCostRecognized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cost recognized, defined contribution plan</link:label>
    <link:label id="lab_us-gaap_DefinedContributionPlanCostRecognized_label_en-US" xlink:label="lab_us-gaap_DefinedContributionPlanCostRecognized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Contribution Plan, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedContributionPlanCostRecognized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DefinedContributionPlanCostRecognized"/>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetBeforeAccumulatedDepreciationAndAmortization_84133d7e-e9e1-4f6b-b13d-74344f9b2022_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetBeforeAccumulatedDepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, plant and equipment, gross</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetBeforeAccumulatedDepreciationAndAmortization_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetBeforeAccumulatedDepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment and Finance Lease Right-of-Use Asset, before Accumulated Depreciation and Amortization</link:label>
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    <link:label id="lab_us-gaap_IncomeTaxAuthorityDomain_60a7de07-bcfb-4178-9e31-f905262c30c1_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Jurisdiction [Domain]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxAuthorityDomain_label_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Jurisdiction [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxAuthorityDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxAuthorityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxAuthorityDomain" xlink:to="lab_us-gaap_IncomeTaxAuthorityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability_a36355b6-a2b0-46b7-9413-9110d29aed80_terseLabel_en-US" xlink:label="lab_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance leases</link:label>
    <link:label id="lab_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability_label_en-US" xlink:label="lab_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Right-of-Use Asset Obtained in Exchange for Finance Lease Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" xlink:to="lab_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfDividendsCommonStock_265a261a-746f-4632-ab34-6f980b9ee152_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfDividendsCommonStock" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Dividends paid</link:label>
    <link:label id="lab_us-gaap_PaymentsOfDividendsCommonStock_label_en-US" xlink:label="lab_us-gaap_PaymentsOfDividendsCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Ordinary Dividends, Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfDividendsCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsOfDividendsCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfDividendsCommonStock" xlink:to="lab_us-gaap_PaymentsOfDividendsCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentAnnualReport_d85cd290-0032-4a24-bc73-dbd36f835915_terseLabel_en-US" xlink:label="lab_dei_DocumentAnnualReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Annual Report</link:label>
    <link:label id="lab_dei_DocumentAnnualReport_label_en-US" xlink:label="lab_dei_DocumentAnnualReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Annual Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentAnnualReport" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentAnnualReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentAnnualReport" xlink:to="lab_dei_DocumentAnnualReport" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_CashPaidForAmountsIncludedInTheMeasurementOfLeaseLiabilitiesAbstract_8d3f0aca-48fb-43de-be6a-6c82b496da5d_terseLabel_en-US" xlink:label="lab_kai_CashPaidForAmountsIncludedInTheMeasurementOfLeaseLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash Paid for Amounts Included in the Measurement of Lease Liabilities:</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_kai_CashPaidForAmountsIncludedInTheMeasurementOfLeaseLiabilitiesAbstract" xlink:href="kai-20260103.xsd#kai_CashPaidForAmountsIncludedInTheMeasurementOfLeaseLiabilitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_CashPaidForAmountsIncludedInTheMeasurementOfLeaseLiabilitiesAbstract" xlink:to="lab_kai_CashPaidForAmountsIncludedInTheMeasurementOfLeaseLiabilitiesAbstract" xlink:type="arc" order="1"/>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock"/>
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    <link:label id="lab_dei_EntityInteractiveDataCurrent_58909af8-9ebb-4a22-b0a4-c5d440682b2e_terseLabel_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityInteractiveDataCurrent" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityInteractiveDataCurrent"/>
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    <link:label id="lab_kai_AuditInformationAbstract_label_en-US" xlink:label="lab_kai_AuditInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Audit Information [Abstract]</link:label>
    <link:label id="lab_kai_AuditInformationAbstract_documentation_en-US" xlink:label="lab_kai_AuditInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Audit Information</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_AuditInformationAbstract" xlink:href="kai-20260103.xsd#kai_AuditInformationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_AuditInformationAbstract" xlink:to="lab_kai_AuditInformationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpenseShareBasedCompensationCost_019bb2b3-21ce-75c9-a3ba-b8185d4265e3_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpenseShareBasedCompensationCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nondeductible Compensation</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReconciliationNondeductibleExpenseShareBasedCompensationCost" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationNondeductibleExpenseShareBasedCompensationCost"/>
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    <link:label id="lab_kai_BusinessCombinationConsiderationTransferredLiabilitiesIncurredNet_30126a40-6f3d-41e3-a587-cdd5f640dafa_terseLabel_en-US" xlink:label="lab_kai_BusinessCombinationConsiderationTransferredLiabilitiesIncurredNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Post-Closing Adjustments</link:label>
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    <link:label id="lab_us-gaap_DisaggregationOfRevenueTable_bb045b53-b0ae-44b8-8612-24ece5187759_terseLabel_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Table]</link:label>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueTable_label_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisaggregationOfRevenueTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisaggregationOfRevenueTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisaggregationOfRevenueTable" xlink:to="lab_us-gaap_DisaggregationOfRevenueTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards_1aa9ff5c-9bd5-4b9e-845a-8f5c9b18073e_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net operating loss carryforwards</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Operating Loss Carryforwards</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsOperatingLossCarryforwards"/>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis_96d54ce6-3a52-4e61-ba5f-74c96886eb37_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Lived Tangible Asset [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentByTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_LineOfCreditFacilityMaximumUnrestrictedCash_019b8243-c105-7aa8-a18f-a489b75f6d9f_terseLabel_en-US" xlink:label="lab_kai_LineOfCreditFacilityMaximumUnrestrictedCash" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum amount of unrestricted cash</link:label>
    <link:label id="lab_kai_LineOfCreditFacilityMaximumUnrestrictedCash_label_en-US" xlink:label="lab_kai_LineOfCreditFacilityMaximumUnrestrictedCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line Of Credit Facility Maximum Unrestricted Cash</link:label>
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    <link:label id="lab_srt_OwnershipDomain_09f4feec-abca-4459-a24f-ef128cb7108b_terseLabel_en-US" xlink:label="lab_srt_OwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership [Domain]</link:label>
    <link:label id="lab_srt_OwnershipDomain_label_en-US" xlink:label="lab_srt_OwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ownership [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_OwnershipDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_OwnershipDomain"/>
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    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo_dbea08be-27c6-4cd0-82d0-d0f2463abf60_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo" xlink:to="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseRightOfUseAssetAccumulatedAmortization_309ba793-4118-4de5-af14-d91998876f7d_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseRightOfUseAssetAccumulatedAmortization" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">ROU assets accumulated amortization</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseRightOfUseAssetAccumulatedAmortization_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseRightOfUseAssetAccumulatedAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Right-of-Use Asset, Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseRightOfUseAssetAccumulatedAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseRightOfUseAssetAccumulatedAmortization"/>
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    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy_5ec72f69-6a31-42be-902d-0abd23f78d49_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy_label_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill and Intangible Assets, Goodwill, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:to="lab_us-gaap_GoodwillAndIntangibleAssetsGoodwillPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BankAcceptancesExecuted_ad70a90c-9e67-4406-92d1-f63c8ad216bf_terseLabel_en-US" xlink:label="lab_us-gaap_BankAcceptancesExecuted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Banker's acceptances drafts</link:label>
    <link:label id="lab_us-gaap_BankAcceptancesExecuted_label_en-US" xlink:label="lab_us-gaap_BankAcceptancesExecuted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Bank Acceptances Executed</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BankAcceptancesExecuted" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BankAcceptancesExecuted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BankAcceptancesExecuted" xlink:to="lab_us-gaap_BankAcceptancesExecuted" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_NoncashOrPartNoncashAcquisitionContingentConsideration_05f3171b-e993-4d5b-b893-9ead75e5c6c3_terseLabel_en-US" xlink:label="lab_kai_NoncashOrPartNoncashAcquisitionContingentConsideration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value of contingent consideration acquired</link:label>
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    <link:label id="lab_kai_NoncashOrPartNoncashAcquisitionContingentConsideration_documentation_en-US" xlink:label="lab_kai_NoncashOrPartNoncashAcquisitionContingentConsideration" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Noncash or Part Noncash Acquisition, Contingent Consideration</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_NoncashOrPartNoncashAcquisitionContingentConsideration" xlink:to="lab_kai_NoncashOrPartNoncashAcquisitionContingentConsideration" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAssetsNoncurrent_21824392-dc42-4a4b-893e-31d03d185512_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherAssetsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other Assets</link:label>
    <link:label id="lab_us-gaap_OtherAssetsNoncurrent_label_en-US" xlink:label="lab_us-gaap_OtherAssetsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssetsNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherAssetsNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssetsNoncurrent" xlink:to="lab_us-gaap_OtherAssetsNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCentralIndexKey_98690cda-19dc-459b-8d29-ab8fd5fd3437_terseLabel_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:label id="lab_dei_EntityCentralIndexKey_label_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCentralIndexKey"/>
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    <link:label id="lab_kai_IndefiniteLivedIntangibleAssetsAccumulatedForeignCurrencyTranslationGainLoss_17ad253a-b3c8-49d3-b26a-af3da6db8360_terseLabel_en-US" xlink:label="lab_kai_IndefiniteLivedIntangibleAssetsAccumulatedForeignCurrencyTranslationGainLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Currency Translation</link:label>
    <link:label id="lab_kai_IndefiniteLivedIntangibleAssetsAccumulatedForeignCurrencyTranslationGainLoss_label_en-US" xlink:label="lab_kai_IndefiniteLivedIntangibleAssetsAccumulatedForeignCurrencyTranslationGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Indefinite-Lived Intangible Assets, Accumulated Foreign Currency Translation Gain (Loss)</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_IndefiniteLivedIntangibleAssetsAccumulatedForeignCurrencyTranslationGainLoss" xlink:to="lab_kai_IndefiniteLivedIntangibleAssetsAccumulatedForeignCurrencyTranslationGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoName_terseLabel_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeoName"/>
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    <link:label id="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock_0c4d14bf-da26-4918-bd15-9b94fb3459b2_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of repayments of long-term debt</link:label>
    <link:label id="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Maturities of Long-Term Debt [Table Text Block]</link:label>
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    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year</link:label>
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    <link:label id="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_ca9866ec-9708-4923-9b5d-55b909c330b5_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems"/>
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    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingAggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_OutstandingAggtErrCompAmt"/>
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    <link:label id="lab_us-gaap_InventoryWorkInProcessNetOfReserves_fef6627f-a9a4-4764-b42e-12a8300d368c_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryWorkInProcessNetOfReserves" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Work in Process</link:label>
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    <link:label id="lab_kai_RightOfUseAssetsObtainedInExchangeForLeaseObligationsAbstract_fa016423-31a4-478b-8575-552955eec07e_terseLabel_en-US" xlink:label="lab_kai_RightOfUseAssetsObtainedInExchangeForLeaseObligationsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">ROU Assets Obtained in Exchange for Lease Obligations:</link:label>
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    <link:label id="lab_kai_FacilityAndOtherClosureCostsMember_147fc351-7b1f-4002-9b82-c1cc0ce02d8f_terseLabel_en-US" xlink:label="lab_kai_FacilityAndOtherClosureCostsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Facility and Other Closure Costs</link:label>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_5cec5906-36bf-4582-9dee-378ec29f7b37_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
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    <link:label id="lab_kai_DeferredTaxLiabilitiesRightofUseAssets_796838a1-ae14-4295-96d5-34498fba2c58_negatedTerseLabel_en-US" xlink:label="lab_kai_DeferredTaxLiabilitiesRightofUseAssets" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">ROU assets</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_kai_DeferredTaxLiabilitiesRightofUseAssets" xlink:href="kai-20260103.xsd#kai_DeferredTaxLiabilitiesRightofUseAssets"/>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsGross_90bef008-9a5c-49ae-aad5-6c40de27aa27_verboseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Gross</link:label>
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    <link:label id="lab_kai_IntangibleAssetsExcludingGoodwillAccumulatedForeignCurrencyTranslationGainLoss_label_en-US" xlink:label="lab_kai_IntangibleAssetsExcludingGoodwillAccumulatedForeignCurrencyTranslationGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Assets, Excluding Goodwill, Accumulated Foreign Currency Translation Gain (Loss)</link:label>
    <link:label id="lab_kai_IntangibleAssetsExcludingGoodwillAccumulatedForeignCurrencyTranslationGainLoss_documentation_en-US" xlink:label="lab_kai_IntangibleAssetsExcludingGoodwillAccumulatedForeignCurrencyTranslationGainLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Intangible Assets, Excluding Goodwill, Accumulated Foreign Currency Translation Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_IntangibleAssetsExcludingGoodwillAccumulatedForeignCurrencyTranslationGainLoss" xlink:href="kai-20260103.xsd#kai_IntangibleAssetsExcludingGoodwillAccumulatedForeignCurrencyTranslationGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_IntangibleAssetsExcludingGoodwillAccumulatedForeignCurrencyTranslationGainLoss" xlink:to="lab_kai_IntangibleAssetsExcludingGoodwillAccumulatedForeignCurrencyTranslationGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote</link:label>
    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_label_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChangedPeerGroupFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ChangedPeerGroupFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChangedPeerGroupFnTextBlock" xlink:to="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_ee9e0ace-9eba-4fc2-8a7d-1c851e6fc958_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StandardProductWarrantyAccrualPayments_a611d702-1c46-456f-bc6a-49821e538832_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_StandardProductWarrantyAccrualPayments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Usage</link:label>
    <link:label id="lab_us-gaap_StandardProductWarrantyAccrualPayments_label_en-US" xlink:label="lab_us-gaap_StandardProductWarrantyAccrualPayments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Standard Product Warranty Accrual, Decrease for Payments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StandardProductWarrantyAccrualPayments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StandardProductWarrantyAccrualPayments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StandardProductWarrantyAccrualPayments" xlink:to="lab_us-gaap_StandardProductWarrantyAccrualPayments" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote</link:label>
    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToPeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AdjToPeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToPeoCompFnTextBlock" xlink:to="lab_ecd_AdjToPeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_FinanceLeasesAbstract_c74e323c-a0d9-4baa-8856-8e5616feb67c_terseLabel_en-US" xlink:label="lab_kai_FinanceLeasesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance Leases:</link:label>
    <link:label id="lab_kai_FinanceLeasesAbstract_label_en-US" xlink:label="lab_kai_FinanceLeasesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Leases [Abstract]</link:label>
    <link:label id="lab_kai_FinanceLeasesAbstract_documentation_en-US" xlink:label="lab_kai_FinanceLeasesAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Finance Leases [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_FinanceLeasesAbstract" xlink:href="kai-20260103.xsd#kai_FinanceLeasesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_FinanceLeasesAbstract" xlink:to="lab_kai_FinanceLeasesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_country_DE_c76ab3c3-50b8-4c25-adc7-edd75bde398a_terseLabel_en-US" xlink:label="lab_country_DE" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Germany</link:label>
    <link:label id="lab_country_DE_label_en-US" xlink:label="lab_country_DE" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">GERMANY</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_country_DE" xlink:href="https://xbrl.sec.gov/country/2025/country-2025.xsd#country_DE"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_country_DE" xlink:to="lab_country_DE" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndTitle_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title</link:label>
    <link:label id="lab_ecd_TrdArrIndTitle_label_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Title</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndTitle" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrIndTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndTitle" xlink:to="lab_ecd_TrdArrIndTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeerGroupTotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:to="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireBusinessesGross_45915c7a-8cc5-44eb-8165-96985baa28bb_verboseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireBusinessesGross" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Cash paid</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireBusinessesGross_a280625c-0de2-4347-a413-2b44f24b018a_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireBusinessesGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash Paid</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireBusinessesGross_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireBusinessesGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Businesses, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireBusinessesGross" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireBusinessesGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireBusinessesGross" xlink:to="lab_us-gaap_PaymentsToAcquireBusinessesGross" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoMember_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO</link:label>
    <link:label id="lab_ecd_NonPeoNeoMember_label_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonPeoNeoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoMember" xlink:to="lab_ecd_NonPeoNeoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LettersOfCreditOutstandingAmount_2492ea2e-d3df-4af2-864b-9b9a86e6c062_terseLabel_en-US" xlink:label="lab_us-gaap_LettersOfCreditOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding letters of credit and bank guarantees</link:label>
    <link:label id="lab_us-gaap_LettersOfCreditOutstandingAmount_label_en-US" xlink:label="lab_us-gaap_LettersOfCreditOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Letters of Credit Outstanding, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LettersOfCreditOutstandingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LettersOfCreditOutstandingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LettersOfCreditOutstandingAmount" xlink:to="lab_us-gaap_LettersOfCreditOutstandingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_country_BR_019bb2be-a047-7fd2-b188-54272d91abc5_terseLabel_en-US" xlink:label="lab_country_BR" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Brazil</link:label>
    <link:label id="lab_country_BR_label_en-US" xlink:label="lab_country_BR" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">BRAZIL</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_country_BR" xlink:href="https://xbrl.sec.gov/country/2025/country-2025.xsd#country_BR"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_country_BR" xlink:to="lab_country_BR" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsSubjectToExpiration_6f3f571d-801e-4790-b64c-813a3031f4f3_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsSubjectToExpiration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating loss carryforwards, subject to expiration</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsSubjectToExpiration_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsSubjectToExpiration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Operating Loss Carryforwards, Subject to Expiration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsSubjectToExpiration" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsSubjectToExpiration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsSubjectToExpiration" xlink:to="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsSubjectToExpiration" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems_c5c63722-2791-48d8-ba0b-90b2c5759f01_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Items [Line Items]</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_OtherCostsIncome_019caec2-66f2-7a2d-9b0e-f46de5d48ec0_terseLabel_en-US" xlink:label="lab_kai_OtherCostsIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Costs (Income)</link:label>
    <link:label id="lab_kai_OtherCostsIncome_label_en-US" xlink:label="lab_kai_OtherCostsIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Costs (Income)</link:label>
    <link:label id="lab_kai_OtherCostsIncome_documentation_en-US" xlink:label="lab_kai_OtherCostsIncome" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Costs (Income)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_OtherCostsIncome" xlink:href="kai-20260103.xsd#kai_OtherCostsIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_OtherCostsIncome" xlink:to="lab_kai_OtherCostsIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherIntangibleAssetsMember_9f2f0f0f-cbae-4814-99ae-cca3a17b3133_terseLabel_en-US" xlink:label="lab_us-gaap_OtherIntangibleAssetsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_OtherIntangibleAssetsMember_label_en-US" xlink:label="lab_us-gaap_OtherIntangibleAssetsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Intangible Assets [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherIntangibleAssetsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherIntangibleAssetsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherIntangibleAssetsMember" xlink:to="lab_us-gaap_OtherIntangibleAssetsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LandMember_74ca264a-2497-4d9b-9e02-d6ebc069a6d5_terseLabel_en-US" xlink:label="lab_us-gaap_LandMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Land</link:label>
    <link:label id="lab_us-gaap_LandMember_label_en-US" xlink:label="lab_us-gaap_LandMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Land [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LandMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LandMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LandMember" xlink:to="lab_us-gaap_LandMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetPriorServiceCostCreditMember_4102a4c0-3160-43f5-97c6-e9c9a08f1132_verboseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetPriorServiceCostCreditMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Amortization of prior service cost, net</link:label>
    <link:label id="lab_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetPriorServiceCostCreditMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetPriorServiceCostCreditMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Defined Benefit Plans Adjustment, Net Prior Service Attributable to Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetPriorServiceCostCreditMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetPriorServiceCostCreditMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetPriorServiceCostCreditMember" xlink:to="lab_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetPriorServiceCostCreditMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_d2c2da71-8ffb-4781-acc9-b3ce007b78bb_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_edbd90db-fc63-491c-aa22-5510167b9afb_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterest_59e85782-4755-4e5e-9082-fc9525d231bd_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncontrolling interests</link:label>
    <link:label id="lab_us-gaap_MinorityInterest_label_en-US" xlink:label="lab_us-gaap_MinorityInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MinorityInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterest" xlink:to="lab_us-gaap_MinorityInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_EqtyAwrdsAdjsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjsMember" xlink:to="lab_ecd_EqtyAwrdsAdjsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNoncashIncomeExpense_4cda7c3f-4a65-4a0b-8a9b-237dfeef9a44_negatedLabel_en-US" xlink:label="lab_us-gaap_OtherNoncashIncomeExpense" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Other items, net</link:label>
    <link:label id="lab_us-gaap_OtherNoncashIncomeExpense_label_en-US" xlink:label="lab_us-gaap_OtherNoncashIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Noncash Income (Expense)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNoncashIncomeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherNoncashIncomeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNoncashIncomeExpense" xlink:to="lab_us-gaap_OtherNoncashIncomeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote</link:label>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_label_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PnsnBnftsAdjFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:to="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherIncome_1caa753f-9c4f-42e9-9e41-be61fedd8bed_terseLabel_en-US" xlink:label="lab_us-gaap_OtherIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other income</link:label>
    <link:label id="lab_us-gaap_OtherIncome_label_en-US" xlink:label="lab_us-gaap_OtherIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherIncome" xlink:to="lab_us-gaap_OtherIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueLineItems_ff241e21-ba0d-4639-b4d9-658f3e67c689_terseLabel_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Line Items]</link:label>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueLineItems_label_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisaggregationOfRevenueLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisaggregationOfRevenueLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisaggregationOfRevenueLineItems" xlink:to="lab_us-gaap_DisaggregationOfRevenueLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_country_CA_23828f73-782a-446e-aadd-ee9a911bcb98_terseLabel_en-US" xlink:label="lab_country_CA" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Canada</link:label>
    <link:label id="lab_country_CA_label_en-US" xlink:label="lab_country_CA" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">CANADA</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_country_CA" xlink:href="https://xbrl.sec.gov/country/2025/country-2025.xsd#country_CA"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_country_CA" xlink:to="lab_country_CA" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_OutstandingRecoveryCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryCompAmt" xlink:to="lab_ecd_OutstandingRecoveryCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract_55e8901f-198a-4e85-be69-f027c78379c9_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred Provision (Benefit)</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Income Tax Expense (Benefit), Continuing Operations [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:to="lab_us-gaap_DeferredIncomeTaxExpenseBenefitContinuingOperationsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_26b488ec-5a5f-4dee-a674-ed222b8df716_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentNameDomain" xlink:to="lab_us-gaap_DebtInstrumentNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RecoveryOfErrCompDisclosureLineItems_label_en-US" xlink:label="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Recovery of Erroneously Awarded Compensation Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_RecoveryOfErrCompDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:to="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember_a20fd60f-a559-4f07-a208-7bb8a23a0269_terseLabel_en-US" xlink:label="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value</link:label>
    <link:label id="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Estimate of Fair Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EstimateOfFairValueFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:to="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerLiabilityRevenueRecognized_f68f2af7-914b-49b5-9486-96c4c0b667e1_terseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiabilityRevenueRecognized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue recognized from contract liabilities</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerLiabilityRevenueRecognized_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiabilityRevenueRecognized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract with Customer, Liability, Revenue Recognized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerLiabilityRevenueRecognized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ContractWithCustomerLiabilityRevenueRecognized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerLiabilityRevenueRecognized" xlink:to="lab_us-gaap_ContractWithCustomerLiabilityRevenueRecognized" xlink:type="arc" order="1"/>
    <link:label id="lab_country_CN_729d91c0-971d-4d38-aef0-b32754b33970_terseLabel_en-US" xlink:label="lab_country_CN" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">China</link:label>
    <link:label id="lab_country_CN_label_en-US" xlink:label="lab_country_CN" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">CHINA</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_country_CN" xlink:href="https://xbrl.sec.gov/country/2025/country-2025.xsd#country_CN"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_country_CN" xlink:to="lab_country_CN" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_terseLabel_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value</link:label>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_label_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_MnpiDiscTimedForCompValFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:to="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTaxAbstract_2ffe7760-aae4-4f4e-ad70-60a3c4b2ecd6_terseLabel_en-US" xlink:label="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTaxAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTaxAbstract_label_en-US" xlink:label="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTaxAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI Including Portion Attributable to Noncontrolling Interest, Net of Tax [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTaxAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTaxAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTaxAbstract" xlink:to="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTaxAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential_019bb2b5-9497-7b4e-9dc0-bf5084a3aeec_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign tax rate differential</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Foreign Income Tax Rate Differential, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential" xlink:to="lab_us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_ImpairmentLongLivedAssetHeldForUseNonCash_019c7c1a-c129-7e9f-b9cd-af425aaa3853_terseLabel_en-US" xlink:label="lab_kai_ImpairmentLongLivedAssetHeldForUseNonCash" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recognized an impairment charge non-cash</link:label>
    <link:label id="lab_kai_ImpairmentLongLivedAssetHeldForUseNonCash_label_en-US" xlink:label="lab_kai_ImpairmentLongLivedAssetHeldForUseNonCash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Impairment, Long-Lived Asset, Held-for-Use, Non-Cash</link:label>
    <link:label id="lab_kai_ImpairmentLongLivedAssetHeldForUseNonCash_documentation_en-US" xlink:label="lab_kai_ImpairmentLongLivedAssetHeldForUseNonCash" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Impairment, Long-Lived Asset, Held-for-Use, Non-Cash</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_ImpairmentLongLivedAssetHeldForUseNonCash" xlink:href="kai-20260103.xsd#kai_ImpairmentLongLivedAssetHeldForUseNonCash"/>
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    <link:label id="lab_us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1_60891829-1240-4cfb-b7b2-d4e515de6e0c_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contingent consideration</link:label>
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    <link:label id="lab_us-gaap_FinanceLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList_16d7bf48-7a51-4232-bcef-a6b4ee24dddb_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance Lease, Right-of-Use Asset, Statement of Financial Position [Extensible List]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList"/>
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    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_39f90c39-9c2e-4a18-8d8a-4eec35d228d4_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated other comprehensive items (Note 13)</link:label>
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    <link:label id="lab_us-gaap_LongTermDebtAndCapitalLeaseObligations_90c2896f-f197-49d4-81a2-b2ac82c3062b_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtAndCapitalLeaseObligations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Obligations (Note 6)</link:label>
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    <link:label id="lab_us-gaap_LongTermDebtAndCapitalLeaseObligations_label_en-US" xlink:label="lab_us-gaap_LongTermDebtAndCapitalLeaseObligations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt and Lease Obligation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtAndCapitalLeaseObligations" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtAndCapitalLeaseObligations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtAndCapitalLeaseObligations" xlink:to="lab_us-gaap_LongTermDebtAndCapitalLeaseObligations" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnrecognizedTaxBenefitsIncreasesResultingFromForeignCurrencyTranslation_6d0b79c4-27b7-4708-b99a-175bab438b8c_terseLabel_en-US" xlink:label="lab_us-gaap_UnrecognizedTaxBenefitsIncreasesResultingFromForeignCurrencyTranslation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Currency Translation</link:label>
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    <link:label id="lab_us-gaap_GoodwillGross_cb9e190f-66f4-43dd-a5b3-9ea7fd584c88_periodStartLabel_en-US" xlink:label="lab_us-gaap_GoodwillGross" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Gross balance, beginning balance</link:label>
    <link:label id="lab_us-gaap_GoodwillGross_07b88b2d-d99e-431d-bb81-d29362f0cb87_periodEndLabel_en-US" xlink:label="lab_us-gaap_GoodwillGross" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Gross balance, ending balance</link:label>
    <link:label id="lab_us-gaap_GoodwillGross_10d883c6-0ff1-47be-9e79-96e97c1effa3_netLabel_en-US" xlink:label="lab_us-gaap_GoodwillGross" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Gross balance</link:label>
    <link:label id="lab_us-gaap_GoodwillGross_label_en-US" xlink:label="lab_us-gaap_GoodwillGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill, Gross</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillGross" xlink:to="lab_us-gaap_GoodwillGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_5703653c-4c79-4c8c-86c9-25c795f6460e_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year One</link:label>
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    <link:label id="lab_kai_ContractWithCustomerLiabilityCurrentAdvancedBillings_bd197309-5655-4e1d-aef6-72e6ae16463b_terseLabel_en-US" xlink:label="lab_kai_ContractWithCustomerLiabilityCurrentAdvancedBillings" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Advanced billings</link:label>
    <link:label id="lab_kai_ContractWithCustomerLiabilityCurrentAdvancedBillings_label_en-US" xlink:label="lab_kai_ContractWithCustomerLiabilityCurrentAdvancedBillings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract With Customer Liability, Current, Advanced Billings</link:label>
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    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilities_be77d720-2495-4de1-9d97-663f65c8e87a_negatedTotalLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilities" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Deferred tax liability</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilities_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredIncomeTaxLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxLiabilities" xlink:to="lab_us-gaap_DeferredIncomeTaxLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive_76841734-542e-4f8c-b681-1860082caeef_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFive"/>
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    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTaxAbstract_6af2d04d-db8d-4d0b-947b-a90dfddbac65_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTaxAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss), Net of Tax [Abstract]</link:label>
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    <link:label id="lab_ecd_AggtPnsnAdjsSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_AggtPnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Pension Adjustments Service Cost</link:label>
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    <link:label id="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpenseOther_019bb2ab-b494-75e6-8b08-4ead2c9f8344_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpenseOther" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other, nontaxable or nondeductible items</link:label>
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    <link:label id="lab_us-gaap_InventoryNet_aaf02e2b-548e-44f4-a4c2-85559670c6e8_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Inventories</link:label>
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    <link:label id="lab_us-gaap_InventoryNet_label_en-US" xlink:label="lab_us-gaap_InventoryNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Inventory, Net</link:label>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_6a8f3520-663b-4bad-9ca7-62f13884860a_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets by Major Class [Axis]</link:label>
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    <link:label id="lab_srt_MinimumMember_dadef6f0-6fdf-42b6-9f85-6d2d8d7153c3_terseLabel_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum</link:label>
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    <link:label id="lab_kai_LineOfCreditFacilityAdditionalBorrowingCapacity_c3cb26ae-2f64-46b1-8dc0-c572fabb6137_terseLabel_en-US" xlink:label="lab_kai_LineOfCreditFacilityAdditionalBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Uncommitted unsecured additional borrowing capacity</link:label>
    <link:label id="lab_kai_LineOfCreditFacilityAdditionalBorrowingCapacity_label_en-US" xlink:label="lab_kai_LineOfCreditFacilityAdditionalBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Additional Borrowing Capacity</link:label>
    <link:label id="lab_kai_LineOfCreditFacilityAdditionalBorrowingCapacity_documentation_en-US" xlink:label="lab_kai_LineOfCreditFacilityAdditionalBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The additional amount available over and above the maximum borrowing capacity under the credit facility.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_LineOfCreditFacilityAdditionalBorrowingCapacity" xlink:href="kai-20260103.xsd#kai_LineOfCreditFacilityAdditionalBorrowingCapacity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_LineOfCreditFacilityAdditionalBorrowingCapacity" xlink:to="lab_kai_LineOfCreditFacilityAdditionalBorrowingCapacity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillPurchaseAccountingAdjustments_4c85b335-c036-41b0-a4cd-fe7e8e8f66c2_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillPurchaseAccountingAdjustments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill measurement period adjustment</link:label>
    <link:label id="lab_us-gaap_GoodwillPurchaseAccountingAdjustments_label_en-US" xlink:label="lab_us-gaap_GoodwillPurchaseAccountingAdjustments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill, Measurement Period Adjustment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillPurchaseAccountingAdjustments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillPurchaseAccountingAdjustments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillPurchaseAccountingAdjustments" xlink:to="lab_us-gaap_GoodwillPurchaseAccountingAdjustments" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureName_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureName_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CoSelectedMeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureName" xlink:to="lab_ecd_CoSelectedMeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosureItemAmountsDomain_f0fab5ec-e1de-4640-8d74-fb78853d947b_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurement [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosureItemAmountsDomain_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosureItemAmountsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:to="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss_c6ee9e06-f795-47c8-b473-355f27c97547_verboseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net Income Attributable to Kadant</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Pro Forma Information, Pro Forma Income (Loss), after Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss" xlink:to="lab_us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_f354d054-1e85-47d7-88ac-98747c123ca9_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Obligations</link:label>
    <link:label id="lab_us-gaap_DebtDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureTextBlock" xlink:to="lab_us-gaap_DebtDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_terseLabel_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Available</link:label>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_label_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Securities Aggregate Available Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrSecuritiesAggAvailAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:to="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsPayableCurrent_3875d240-7e8d-462c-a912-bb50b04822e8_verboseLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Accounts payable</link:label>
    <link:label id="lab_us-gaap_AccountsPayableCurrent_label_en-US" xlink:label="lab_us-gaap_AccountsPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Payable, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsPayableCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsPayableCurrent" xlink:to="lab_us-gaap_AccountsPayableCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeasePayments_c709dfde-d599-4291-b574-4190e45f5181_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeasePayments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating cash flows from operating leases</link:label>
    <link:label id="lab_us-gaap_OperatingLeasePayments_label_en-US" xlink:label="lab_us-gaap_OperatingLeasePayments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Payments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeasePayments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeasePayments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeasePayments" xlink:to="lab_us-gaap_OperatingLeasePayments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StandardProductWarrantyAccrualWarrantiesIssued_49ddecfa-076e-4ec7-987b-6ae81103950b_terseLabel_en-US" xlink:label="lab_us-gaap_StandardProductWarrantyAccrualWarrantiesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Provision charged to expense</link:label>
    <link:label id="lab_us-gaap_StandardProductWarrantyAccrualWarrantiesIssued_label_en-US" xlink:label="lab_us-gaap_StandardProductWarrantyAccrualWarrantiesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Standard Product Warranty Accrual, Increase for Warranties Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StandardProductWarrantyAccrualWarrantiesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StandardProductWarrantyAccrualWarrantiesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StandardProductWarrantyAccrualWarrantiesIssued" xlink:to="lab_us-gaap_StandardProductWarrantyAccrualWarrantiesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_terseLabel_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs)</link:label>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_label_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockAppreciationRightsSARSMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:to="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsPayableCurrentAndNoncurrent_b7d22ed5-b083-42b6-8f24-5d080648f386_terseLabel_en-US" xlink:label="lab_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends declared but unpaid</link:label>
    <link:label id="lab_us-gaap_DividendsPayableCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DividendsPayableCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:to="lab_us-gaap_DividendsPayableCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ImpairmentOfIntangibleAssetsExcludingGoodwill_f8d791df-1c97-4172-90d6-7a6b1d3fd4a1_terseLabel_en-US" xlink:label="lab_us-gaap_ImpairmentOfIntangibleAssetsExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other non-cash costs (Note 8)</link:label>
    <link:label id="lab_us-gaap_ImpairmentOfIntangibleAssetsExcludingGoodwill_label_en-US" xlink:label="lab_us-gaap_ImpairmentOfIntangibleAssetsExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Impairment of Intangible Assets (Excluding Goodwill)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ImpairmentOfIntangibleAssetsExcludingGoodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ImpairmentOfIntangibleAssetsExcludingGoodwill"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ImpairmentOfIntangibleAssetsExcludingGoodwill" xlink:to="lab_us-gaap_ImpairmentOfIntangibleAssetsExcludingGoodwill" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CurrentForeignTaxExpenseBenefit_cf4cfc55-3f41-4c31-91c1-10c11bb5ace7_terseLabel_en-US" xlink:label="lab_us-gaap_CurrentForeignTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign</link:label>
    <link:label id="lab_us-gaap_CurrentForeignTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_CurrentForeignTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Foreign Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CurrentForeignTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CurrentForeignTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CurrentForeignTaxExpenseBenefit" xlink:to="lab_us-gaap_CurrentForeignTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestructuringPlanDomain_1a7e841e-0a6a-4eb0-bddf-a5afe5ec1f8d_terseLabel_en-US" xlink:label="lab_us-gaap_RestructuringPlanDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restructuring Plan [Domain]</link:label>
    <link:label id="lab_us-gaap_RestructuringPlanDomain_label_en-US" xlink:label="lab_us-gaap_RestructuringPlanDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restructuring Plan [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestructuringPlanDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestructuringPlanDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestructuringPlanDomain" xlink:to="lab_us-gaap_RestructuringPlanDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillRollForward_db8e634f-54a4-401b-9096-a5bcb811f8c8_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_GoodwillRollForward_label_en-US" xlink:label="lab_us-gaap_GoodwillRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillRollForward" xlink:to="lab_us-gaap_GoodwillRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_2cd5c9ec-9fa9-4f05-81a4-d02198b01501_verboseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommitmentsAndContingenciesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:to="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_722656d3-a379-4767-8817-2f8cbb044c1a_verboseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Diluted (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_2e7fe487-2b5a-4030-92e6-0c05f98f1bb0_totalLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Diluted Weighted Average Shares</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:to="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock_8709de86-9c2e-489d-973f-e003b0be0ce0_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting</link:label>
    <link:label id="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:to="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonGaapMeasureDescriptionTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-GAAP Measure Description</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShortTermLeaseCost" xlink:to="lab_us-gaap_ShortTermLeaseCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList_4b1362fb-a712-44a4-8a98-96be0eaff5a8_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Noncurrent, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Noncurrent, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList" xlink:to="lab_us-gaap_OperatingLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_14b55641-5227-4baa-91d2-22c50a9793ee_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Stockholders' Equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_2ba18f8b-3cad-4872-b3e8-9b8dd39424b9_periodStartLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_bd1f561f-79fc-4b0a-afac-d24ed1251ec5_periodEndLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Including Portion Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:to="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentType_d7c1c145-66f8-4657-937e-be58ed69c094_terseLabel_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
    <link:label id="lab_dei_DocumentType_label_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentType" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentType"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentType" xlink:to="lab_dei_DocumentType" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_0c6867e3-3e9a-41ba-9bcf-03114aa81c0a_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 3</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 3 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel3Member" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel3Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel3Member" xlink:to="lab_us-gaap_FairValueInputsLevel3Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareTextBlock_8745f9b9-bbe8-4304-982f-64d3494346ac_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings per Share</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareTextBlock_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareTextBlock" xlink:to="lab_us-gaap_EarningsPerShareTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_OutstandingRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryIndName" xlink:to="lab_ecd_OutstandingRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalPaidInCapital_022c3cbb-0994-4721-a299-18d636d34002_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Capital in excess of par value</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapital_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid in Capital</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapital" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdditionalPaidInCapital"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapital" xlink:to="lab_us-gaap_AdditionalPaidInCapital" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ProductOrServiceAxis_dd9fd14e-f9bd-465e-b587-284f1fcd74f4_terseLabel_en-US" xlink:label="lab_srt_ProductOrServiceAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product and Service [Axis]</link:label>
    <link:label id="lab_srt_ProductOrServiceAxis_label_en-US" xlink:label="lab_srt_ProductOrServiceAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product and Service [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductOrServiceAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProductOrServiceAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ProductOrServiceAxis" xlink:to="lab_srt_ProductOrServiceAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableLeaseCost_36a6e643-cd4d-4bb2-8f45-2cbf9d429360_terseLabel_en-US" xlink:label="lab_us-gaap_VariableLeaseCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable lease cost</link:label>
    <link:label id="lab_us-gaap_VariableLeaseCost_label_en-US" xlink:label="lab_us-gaap_VariableLeaseCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Lease, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableLeaseCost" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VariableLeaseCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableLeaseCost" xlink:to="lab_us-gaap_VariableLeaseCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_9fbbd5a2-d159-450b-b9c5-eadd17d45e78_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue (Notes 1 and 11)</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_715737ab-6133-41e3-92d9-7c95b12fbf5f_verboseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Revenue</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer, Excluding Assessed Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:to="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsCurrent_35d68878-b7b5-43b7-aa61-363667196bd3_totalLabel_en-US" xlink:label="lab_us-gaap_AssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Current Assets</link:label>
    <link:label id="lab_us-gaap_AssetsCurrent_label_en-US" xlink:label="lab_us-gaap_AssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsCurrent" xlink:to="lab_us-gaap_AssetsCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_DoctoringCleaningAndFiltrationMember_cea4f5c7-bd7a-4d37-ab2b-732e4f47c364_terseLabel_en-US" xlink:label="lab_kai_DoctoringCleaningAndFiltrationMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Doctoring, Cleaning, &amp; Filtration</link:label>
    <link:label id="lab_kai_DoctoringCleaningAndFiltrationMember_label_en-US" xlink:label="lab_kai_DoctoringCleaningAndFiltrationMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Doctoring, Cleaning and Filtration [Member]</link:label>
    <link:label id="lab_kai_DoctoringCleaningAndFiltrationMember_documentation_en-US" xlink:label="lab_kai_DoctoringCleaningAndFiltrationMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Operating segment product line.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_DoctoringCleaningAndFiltrationMember" xlink:href="kai-20260103.xsd#kai_DoctoringCleaningAndFiltrationMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_DoctoringCleaningAndFiltrationMember" xlink:to="lab_kai_DoctoringCleaningAndFiltrationMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeAxis_8716add6-77e8-485d-831a-38b826f9ed9c_terseLabel_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:label id="lab_srt_RangeAxis_label_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeAxis" xlink:to="lab_srt_RangeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinitelivedIntangibleAssetsAcquired1_c652633b-bbf2-49e5-a354-4e366abf79f3_terseLabel_en-US" xlink:label="lab_us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finite-lived intangible assets acquired</link:label>
    <link:label id="lab_us-gaap_FinitelivedIntangibleAssetsAcquired1_label_en-US" xlink:label="lab_us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets Acquired</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinitelivedIntangibleAssetsAcquired1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:to="lab_us-gaap_FinitelivedIntangibleAssetsAcquired1" xlink:type="arc" order="1"/>
    <link:label id="lab_country_FI_dd4327e0-facd-4b4c-86a1-11d4fc2dd0a3_terseLabel_en-US" xlink:label="lab_country_FI" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finland</link:label>
    <link:label id="lab_country_FI_label_en-US" xlink:label="lab_country_FI" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">FINLAND</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_country_FI" xlink:href="https://xbrl.sec.gov/country/2025/country-2025.xsd#country_FI"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_country_FI" xlink:to="lab_country_FI" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_AggtErrCompAmt_label_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompAmt" xlink:to="lab_ecd_AggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation_0596917e-a8e1-4986-892e-6a7b8fcb7fc4_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Tax withholding payments related to stock-based compensation</link:label>
    <link:label id="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment, Tax Withholding, Share-Based Payment Arrangement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:to="lab_us-gaap_PaymentsRelatedToTaxWithholdingForShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote</link:label>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_label_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeerGroupIssuersFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:to="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_FinanceLeaseCostsAbstract_28d663d7-177d-407f-a97e-2bd13b56ae67_terseLabel_en-US" xlink:label="lab_kai_FinanceLeaseCostsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance Lease Cost:</link:label>
    <link:label id="lab_kai_FinanceLeaseCostsAbstract_label_en-US" xlink:label="lab_kai_FinanceLeaseCostsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Costs [Abstract]</link:label>
    <link:label id="lab_kai_FinanceLeaseCostsAbstract_documentation_en-US" xlink:label="lab_kai_FinanceLeaseCostsAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Finance Lease, Costs [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_FinanceLeaseCostsAbstract" xlink:href="kai-20260103.xsd#kai_FinanceLeaseCostsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_FinanceLeaseCostsAbstract" xlink:to="lab_kai_FinanceLeaseCostsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesCurrentAbstract_7ce1085f-a6ff-4bd4-8cbc-2a142d702883_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current Liabilities:</link:label>
    <link:label id="lab_us-gaap_LiabilitiesCurrentAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Current [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesCurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesCurrentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesCurrentAbstract" xlink:to="lab_us-gaap_LiabilitiesCurrentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_NontradeReceivablesCurrentNetOfPresentValueDiscount_019c9880-7167-7570-a3d2-8b88b8506505_terseLabel_en-US" xlink:label="lab_kai_NontradeReceivablesCurrentNetOfPresentValueDiscount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amount of receivable settled by government</link:label>
    <link:label id="lab_kai_NontradeReceivablesCurrentNetOfPresentValueDiscount_label_en-US" xlink:label="lab_kai_NontradeReceivablesCurrentNetOfPresentValueDiscount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nontrade Receivables, Current, Net Of Present Value Discount</link:label>
    <link:label id="lab_kai_NontradeReceivablesCurrentNetOfPresentValueDiscount_documentation_en-US" xlink:label="lab_kai_NontradeReceivablesCurrentNetOfPresentValueDiscount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Nontrade Receivables, Current, Net Of Present Value Discount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_NontradeReceivablesCurrentNetOfPresentValueDiscount" xlink:href="kai-20260103.xsd#kai_NontradeReceivablesCurrentNetOfPresentValueDiscount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_NontradeReceivablesCurrentNetOfPresentValueDiscount" xlink:to="lab_kai_NontradeReceivablesCurrentNetOfPresentValueDiscount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_3bd8931b-98a7-415e-88c2-1ee637de9138_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 1</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 1 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel1Member" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel1Member" xlink:to="lab_us-gaap_FairValueInputsLevel1Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesAccountsPayable_56e22e71-a2cc-4663-893b-5ee4892f836e_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesAccountsPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts Payable</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesAccountsPayable_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesAccountsPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Accounts Payable, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesAccountsPayable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesAccountsPayable"/>
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    <link:label id="lab_kai_MaterialHandlingSystemsMember_7ffe6d46-4b2e-4004-ab57-ec8197de98de_verboseLabel_en-US" xlink:label="lab_kai_MaterialHandlingSystemsMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Material Handling</link:label>
    <link:label id="lab_kai_MaterialHandlingSystemsMember_9fc1a9a1-3d15-4f42-8a61-19022df41cf5_terseLabel_en-US" xlink:label="lab_kai_MaterialHandlingSystemsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Material Handling</link:label>
    <link:label id="lab_kai_MaterialHandlingSystemsMember_label_en-US" xlink:label="lab_kai_MaterialHandlingSystemsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Material Handling Systems [Member]</link:label>
    <link:label id="lab_kai_MaterialHandlingSystemsMember_documentation_en-US" xlink:label="lab_kai_MaterialHandlingSystemsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Material Handling Systems [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_MaterialHandlingSystemsMember" xlink:href="kai-20260103.xsd#kai_MaterialHandlingSystemsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_MaterialHandlingSystemsMember" xlink:to="lab_kai_MaterialHandlingSystemsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_d3457d7e-9155-4a31-9784-6c28744f0de2_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Diluted (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareDiluted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareDiluted" xlink:to="lab_us-gaap_EarningsPerShareDiluted" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationTaxCreditsOther_019bb2ab-b494-793a-81ef-05704962034b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationTaxCreditsOther" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Other, tax credits</link:label>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationTaxCreditsOther_label_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationTaxCreditsOther" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Tax Credit, Other, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReconciliationTaxCreditsOther" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationTaxCreditsOther"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxReconciliationTaxCreditsOther" xlink:to="lab_us-gaap_IncomeTaxReconciliationTaxCreditsOther" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsReceivableNetCurrent_146cb554-2e49-438c-822f-09b5743e5ffd_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableNetCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts receivable, net of allowances of $5,149 and $4,403</link:label>
    <link:label id="lab_us-gaap_AccountsReceivableNetCurrent_label_en-US" xlink:label="lab_us-gaap_AccountsReceivableNetCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, after Allowance for Credit Loss, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsReceivableNetCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountsReceivableNetCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsReceivableNetCurrent" xlink:to="lab_us-gaap_AccountsReceivableNetCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeAxis_1ed433e5-83cd-4a28-a382-872ccd20b664_terseLabel_en-US" xlink:label="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reclassification out of Accumulated Other Comprehensive Income [Axis]</link:label>
    <link:label id="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeAxis_label_en-US" xlink:label="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reclassification out of Accumulated Other Comprehensive Income [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeAxis" xlink:to="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityForeignCurrencyTranslation_c77fa76b-42df-4089-a531-41bc147a8663_negatedLabel_en-US" xlink:label="lab_kai_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityForeignCurrencyTranslation" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Currency translation</link:label>
    <link:label id="lab_kai_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityForeignCurrencyTranslation_label_en-US" xlink:label="lab_kai_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityForeignCurrencyTranslation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement With Unobservable Inputs Reconciliation, Recurring Basis, Liability, Foreign Currency Translation</link:label>
    <link:label id="lab_kai_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityForeignCurrencyTranslation_documentation_en-US" xlink:label="lab_kai_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityForeignCurrencyTranslation" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement With Unobservable Inputs Reconciliation, Recurring Basis, Liability, Foreign Currency Translation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityForeignCurrencyTranslation" xlink:href="kai-20260103.xsd#kai_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityForeignCurrencyTranslation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityForeignCurrencyTranslation" xlink:to="lab_kai_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityForeignCurrencyTranslation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems_41e7cc30-54a0-4b43-af21-009bbaeb2573_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:to="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockCommonShares_b7cb432c-7c12-4bf4-bfa6-b3402a0ac130_terseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Treasury stock (in shares)</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonShares_cf3589dc-47cf-44d1-ba0d-f9e42a4c3536_periodStartLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonShares" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance, treasury (in shares)</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonShares_5f29b7d4-4fa1-4557-aeba-7687577cdcc2_periodEndLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonShares" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance, treasury (in shares)</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonShares_label_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Common, Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockCommonShares" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TreasuryStockCommonShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockCommonShares" xlink:to="lab_us-gaap_TreasuryStockCommonShares" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived_019bb2c1-6e26-73cf-9ca3-8d2686debd7d_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">State</link:label>
    <link:label id="lab_us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived_label_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Paid, State and Local, after Refund Received</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived" xlink:to="lab_us-gaap_IncomeTaxPaidStateAndLocalAfterRefundReceived" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_DeferredTaxAssetsTaxCreditCarryforwardsForeignIncludingAlternativeMinimumTaxCredits_8d5fabe5-de8f-47ee-a711-27732353cdb5_terseLabel_en-US" xlink:label="lab_kai_DeferredTaxAssetsTaxCreditCarryforwardsForeignIncludingAlternativeMinimumTaxCredits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign, state, and alternative minimum tax credit carryforwards</link:label>
    <link:label id="lab_kai_DeferredTaxAssetsTaxCreditCarryforwardsForeignIncludingAlternativeMinimumTaxCredits_label_en-US" xlink:label="lab_kai_DeferredTaxAssetsTaxCreditCarryforwardsForeignIncludingAlternativeMinimumTaxCredits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Tax Credit Carryforwards, Foreign Including Alternative Minimum Tax Credits</link:label>
    <link:label id="lab_kai_DeferredTaxAssetsTaxCreditCarryforwardsForeignIncludingAlternativeMinimumTaxCredits_documentation_en-US" xlink:label="lab_kai_DeferredTaxAssetsTaxCreditCarryforwardsForeignIncludingAlternativeMinimumTaxCredits" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Amount before allocation of valuation allowances of deferred tax asset attributable to deductible foreign tax credit carryforwards and alternative minimum tax credit carryforwards.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_DeferredTaxAssetsTaxCreditCarryforwardsForeignIncludingAlternativeMinimumTaxCredits" xlink:href="kai-20260103.xsd#kai_DeferredTaxAssetsTaxCreditCarryforwardsForeignIncludingAlternativeMinimumTaxCredits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_DeferredTaxAssetsTaxCreditCarryforwardsForeignIncludingAlternativeMinimumTaxCredits" xlink:to="lab_kai_DeferredTaxAssetsTaxCreditCarryforwardsForeignIncludingAlternativeMinimumTaxCredits" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidationItemsDomain_041c24c7-cf22-4d73-9cc5-7fe2c5fe8ca1_terseLabel_en-US" xlink:label="lab_srt_ConsolidationItemsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation Items [Domain]</link:label>
    <link:label id="lab_srt_ConsolidationItemsDomain_label_en-US" xlink:label="lab_srt_ConsolidationItemsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation Items [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidationItemsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidationItemsDomain" xlink:to="lab_srt_ConsolidationItemsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AuditorLocation_42732d8e-a881-4ece-abea-ce57d4a49082_terseLabel_en-US" xlink:label="lab_dei_AuditorLocation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Auditor Location</link:label>
    <link:label id="lab_dei_AuditorLocation_label_en-US" xlink:label="lab_dei_AuditorLocation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Auditor Location</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AuditorLocation" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_AuditorLocation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_AuditorLocation" xlink:to="lab_dei_AuditorLocation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GrossProfit_9d2b805b-0e59-40cf-b6ed-27aeeef40801_totalLabel_en-US" xlink:label="lab_us-gaap_GrossProfit" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Gross Profit</link:label>
    <link:label id="lab_us-gaap_GrossProfit_label_en-US" xlink:label="lab_us-gaap_GrossProfit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gross Profit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GrossProfit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GrossProfit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GrossProfit" xlink:to="lab_us-gaap_GrossProfit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DomesticCountryMember_019bb2ab-b494-7919-8ba5-62abe45af8db_terseLabel_en-US" xlink:label="lab_us-gaap_DomesticCountryMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Domestic Tax Jurisdiction</link:label>
    <link:label id="lab_us-gaap_DomesticCountryMember_label_en-US" xlink:label="lab_us-gaap_DomesticCountryMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Domestic Tax Jurisdiction [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DomesticCountryMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DomesticCountryMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DomesticCountryMember" xlink:to="lab_us-gaap_DomesticCountryMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_BabbiniMember_019b8222-004b-78fb-bfe3-081c76da985c_terseLabel_en-US" xlink:label="lab_kai_BabbiniMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Babbini</link:label>
    <link:label id="lab_kai_BabbiniMember_label_en-US" xlink:label="lab_kai_BabbiniMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Babbini [Member]</link:label>
    <link:label id="lab_kai_BabbiniMember_documentation_en-US" xlink:label="lab_kai_BabbiniMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Babbini</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_BabbiniMember" xlink:href="kai-20260103.xsd#kai_BabbiniMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_BabbiniMember" xlink:to="lab_kai_BabbiniMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_61f33f64-86e6-4fa4-8a39-ef0ebb2f2d6f_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Less: Imputed Interest</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, Undiscounted Excess Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseOther_019bb2ab-b494-770d-a925-d9ef0c2cb060_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseOther" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other, nontaxable or nondeductible items</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseOther_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseOther" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Nondeductible Expense, Other, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseOther" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseOther"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseOther" xlink:to="lab_us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseOther" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxesPaidNet_019bb2c5-5df5-7e91-9de1-0c7dd15761e9_verboseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaidNet" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Cash paid for income taxes, net of refunds</link:label>
    <link:label id="lab_us-gaap_IncomeTaxesPaidNet_019bb2c1-6e26-75ea-a4eb-810f3be94e42_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaidNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total income taxes paid</link:label>
    <link:label id="lab_us-gaap_IncomeTaxesPaidNet_label_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaidNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Taxes Paid, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxesPaidNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxesPaidNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxesPaidNet" xlink:to="lab_us-gaap_IncomeTaxesPaidNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_742682f4-0e45-431b-be7d-c0214f4b13a1_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityWellKnownSeasonedIssuer_8d04985d-b0dc-4939-b05c-86fcbcdd0f07_terseLabel_en-US" xlink:label="lab_dei_EntityWellKnownSeasonedIssuer" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Well-known Seasoned Issuer</link:label>
    <link:label id="lab_dei_EntityWellKnownSeasonedIssuer_label_en-US" xlink:label="lab_dei_EntityWellKnownSeasonedIssuer" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Well-known Seasoned Issuer</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityWellKnownSeasonedIssuer" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityWellKnownSeasonedIssuer"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityWellKnownSeasonedIssuer" xlink:to="lab_dei_EntityWellKnownSeasonedIssuer" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeRelatedLiabilitiesCurrent_8ceedf65-b9b5-48fe-b9b1-b90a1d798656_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued payroll and employee benefits</link:label>
    <link:label id="lab_us-gaap_EmployeeRelatedLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Employee-related Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EmployeeRelatedLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:to="lab_us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_d5c83087-1a03-4644-bd32-e4f686f26f9c_totalLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Future Lease Payments</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization_4e5741b5-870f-4757-ac9a-6ffef4b2e8ff_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment, Net</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization_fb4a7179-0905-4419-85ae-1b06eb7472b0_totalLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Property, plant and equipment, at cost, net</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization_fd59e8fc-c244-4413-8f75-f4bd7ca0fe13_verboseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Long-lived Assets</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment and Finance Lease Right-of-Use Asset, after Accumulated Depreciation and Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity_019b8243-c105-77db-b295-71fb8e43eec7_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Borrowing capacity available under committed portion</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Current Borrowing Capacity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity" xlink:to="lab_us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders_234385f7-72af-45c5-a44d-cb9a2cc64506_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Dividends paid to noncontrolling interests</link:label>
    <link:label id="lab_us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders_label_en-US" xlink:label="lab_us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest, Decrease from Distributions to Noncontrolling Interest Holders</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders" xlink:to="lab_us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_SharebasedCompensationArrangementbySharebasedPaymentAwardSharesReceivedUponVesting_a6a63869-a124-41e2-b5c0-de486e10afbf_terseLabel_en-US" xlink:label="lab_kai_SharebasedCompensationArrangementbySharebasedPaymentAwardSharesReceivedUponVesting" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares received upon vesting (in shares)</link:label>
    <link:label id="lab_kai_SharebasedCompensationArrangementbySharebasedPaymentAwardSharesReceivedUponVesting_label_en-US" xlink:label="lab_kai_SharebasedCompensationArrangementbySharebasedPaymentAwardSharesReceivedUponVesting" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award, Shares Received Upon Vesting</link:label>
    <link:label id="lab_kai_SharebasedCompensationArrangementbySharebasedPaymentAwardSharesReceivedUponVesting_documentation_en-US" xlink:label="lab_kai_SharebasedCompensationArrangementbySharebasedPaymentAwardSharesReceivedUponVesting" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award, Shares Received Upon Vesting</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_SharebasedCompensationArrangementbySharebasedPaymentAwardSharesReceivedUponVesting" xlink:href="kai-20260103.xsd#kai_SharebasedCompensationArrangementbySharebasedPaymentAwardSharesReceivedUponVesting"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_SharebasedCompensationArrangementbySharebasedPaymentAwardSharesReceivedUponVesting" xlink:to="lab_kai_SharebasedCompensationArrangementbySharebasedPaymentAwardSharesReceivedUponVesting" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TradeNamesMember_8ac4bcaf-cda7-4a1a-8ada-4f87a1fb04de_terseLabel_en-US" xlink:label="lab_us-gaap_TradeNamesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tradenames</link:label>
    <link:label id="lab_us-gaap_TradeNamesMember_label_en-US" xlink:label="lab_us-gaap_TradeNamesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trade Names [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TradeNamesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TradeNamesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TradeNamesMember" xlink:to="lab_us-gaap_TradeNamesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrExpirationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrExpirationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expiration Date</link:label>
    <link:label id="lab_ecd_TrdArrExpirationDate_label_en-US" xlink:label="lab_ecd_TrdArrExpirationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Expiration Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrExpirationDate" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrExpirationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrExpirationDate" xlink:to="lab_ecd_TrdArrExpirationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_SegmentGeographicalGroupsOfCountriesOtherCountriesMember_fdbe63e1-d3ee-468c-a815-5cb547212d38_terseLabel_en-US" xlink:label="lab_kai_SegmentGeographicalGroupsOfCountriesOtherCountriesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_kai_SegmentGeographicalGroupsOfCountriesOtherCountriesMember_label_en-US" xlink:label="lab_kai_SegmentGeographicalGroupsOfCountriesOtherCountriesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment, Geographical, Groups of Countries, Other Countries [Member]</link:label>
    <link:label id="lab_kai_SegmentGeographicalGroupsOfCountriesOtherCountriesMember_documentation_en-US" xlink:label="lab_kai_SegmentGeographicalGroupsOfCountriesOtherCountriesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">A specified group of foreign countries about which segment information is provided by the entity. The entity is expected to change the standard label to identify the specified group.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_SegmentGeographicalGroupsOfCountriesOtherCountriesMember" xlink:href="kai-20260103.xsd#kai_SegmentGeographicalGroupsOfCountriesOtherCountriesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_SegmentGeographicalGroupsOfCountriesOtherCountriesMember" xlink:to="lab_kai_SegmentGeographicalGroupsOfCountriesOtherCountriesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_ProductWarrantyAccrualAndInstallationCostsCurrent_d1802fc3-d680-417e-80e4-685308476e36_terseLabel_en-US" xlink:label="lab_kai_ProductWarrantyAccrualAndInstallationCostsCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued warranty and installation costs</link:label>
    <link:label id="lab_kai_ProductWarrantyAccrualAndInstallationCostsCurrent_label_en-US" xlink:label="lab_kai_ProductWarrantyAccrualAndInstallationCostsCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product Warranty Accrual And Installation Costs, Current</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_kai_ProductWarrantyAccrualAndInstallationCostsCurrent" xlink:href="kai-20260103.xsd#kai_ProductWarrantyAccrualAndInstallationCostsCurrent"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFive" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain_32b71115-8457-4e8f-9439-2b23306dfbf0_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Lived Tangible Asset [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CostOfGoodsAndServicesSold_b722b44d-dc15-48a3-9144-fd617143ea50_terseLabel_en-US" xlink:label="lab_us-gaap_CostOfGoodsAndServicesSold" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cost of revenue</link:label>
    <link:label id="lab_us-gaap_CostOfGoodsAndServicesSold_label_en-US" xlink:label="lab_us-gaap_CostOfGoodsAndServicesSold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cost of Product and Service Sold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CostOfGoodsAndServicesSold" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CostOfGoodsAndServicesSold"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CostOfGoodsAndServicesSold" xlink:to="lab_us-gaap_CostOfGoodsAndServicesSold" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetUnamortizedGainLossMember_9d2c916c-e022-438e-b14f-d6ed7ff453a4_verboseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetUnamortizedGainLossMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Recognized actuarial gain (loss), net</link:label>
    <link:label id="lab_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetUnamortizedGainLossMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetUnamortizedGainLossMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Defined Benefit Plans Adjustment, Net Gain (Loss) Attributable to Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetUnamortizedGainLossMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetUnamortizedGainLossMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetUnamortizedGainLossMember" xlink:to="lab_us-gaap_AccumulatedDefinedBenefitPlansAdjustmentNetUnamortizedGainLossMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_NoncontrollingInterestOptionToPurchaseRemainingOwnershipPercentage_c3e9a849-166b-4c9e-94cf-8900ae0ad2d3_terseLabel_en-US" xlink:label="lab_kai_NoncontrollingInterestOptionToPurchaseRemainingOwnershipPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Remaining ownership interest with an option to purchase</link:label>
    <link:label id="lab_kai_NoncontrollingInterestOptionToPurchaseRemainingOwnershipPercentage_label_en-US" xlink:label="lab_kai_NoncontrollingInterestOptionToPurchaseRemainingOwnershipPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest, Option To Purchase, Remaining Ownership Percentage</link:label>
    <link:label id="lab_kai_NoncontrollingInterestOptionToPurchaseRemainingOwnershipPercentage_documentation_en-US" xlink:label="lab_kai_NoncontrollingInterestOptionToPurchaseRemainingOwnershipPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest, Option To Purchase, Remaining Ownership Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_NoncontrollingInterestOptionToPurchaseRemainingOwnershipPercentage" xlink:href="kai-20260103.xsd#kai_NoncontrollingInterestOptionToPurchaseRemainingOwnershipPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_NoncontrollingInterestOptionToPurchaseRemainingOwnershipPercentage" xlink:to="lab_kai_NoncontrollingInterestOptionToPurchaseRemainingOwnershipPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfBusinessesAcquired_019b8222-bf9d-7eed-9272-e0a0d5284302_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfBusinessesAcquired" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of businesses acquired</link:label>
    <link:label id="lab_us-gaap_NumberOfBusinessesAcquired_label_en-US" xlink:label="lab_us-gaap_NumberOfBusinessesAcquired" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Number of Businesses Acquired</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfBusinessesAcquired" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NumberOfBusinessesAcquired"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfBusinessesAcquired" xlink:to="lab_us-gaap_NumberOfBusinessesAcquired" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock_13f759d1-1a36-4d14-a6f4-749600e8c611_terseLabel_en-US" xlink:label="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reclassification out of accumulated other comprehensive items</link:label>
    <link:label id="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reclassification out of Accumulated Other Comprehensive Income [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock" xlink:to="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PvpTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure, Table</link:label>
    <link:label id="lab_ecd_PvpTableTextBlock_label_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PvpTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PvpTableTextBlock" xlink:to="lab_ecd_PvpTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt"/>
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    <link:label id="lab_dei_EntityTaxIdentificationNumber_45f76d5f-a80c-4ec9-9c01-3a2f1d2eba91_terseLabel_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_label_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityTaxIdentificationNumber" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityTaxIdentificationNumber"/>
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    <link:label id="lab_us-gaap_PensionAndOtherPostretirementPlansNonpensionBenefitsPolicy_e96fe27a-5d7e-42c0-9821-f77b2ee8dbee_terseLabel_en-US" xlink:label="lab_us-gaap_PensionAndOtherPostretirementPlansNonpensionBenefitsPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">401(k) Savings and Other Defined Contribution Plans</link:label>
    <link:label id="lab_us-gaap_PensionAndOtherPostretirementPlansNonpensionBenefitsPolicy_label_en-US" xlink:label="lab_us-gaap_PensionAndOtherPostretirementPlansNonpensionBenefitsPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension and Other Postretirement Plans, Nonpension Benefits, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PensionAndOtherPostretirementPlansNonpensionBenefitsPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PensionAndOtherPostretirementPlansNonpensionBenefitsPolicy"/>
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    <link:label id="lab_us-gaap_CommonStockSharesIssued_87511005-2a17-4745-9ab8-e6d4f498ee29_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, issued (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesIssued" xlink:to="lab_us-gaap_CommonStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_3f9329a5-7d6a-4ec3-93a2-c34802931026_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease, weighted average remaining lease term (years)</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Weighted Average Remaining Lease Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:to="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_e111828c-dffc-4533-847a-0b24db6262f9_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour"/>
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    <link:label id="lab_dei_EntityPublicFloat_ac31bff3-96e9-4317-b18a-8784aab5bafb_terseLabel_en-US" xlink:label="lab_dei_EntityPublicFloat" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Public Float</link:label>
    <link:label id="lab_dei_EntityPublicFloat_label_en-US" xlink:label="lab_dei_EntityPublicFloat" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Public Float</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityPublicFloat" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityPublicFloat"/>
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    <link:label id="lab_us-gaap_ScheduleOfGoodwillTextBlock_03e7eca9-9e99-4585-b11a-af1b1b77f6f2_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfGoodwillTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changes in the carrying amount of goodwill by segment</link:label>
    <link:label id="lab_us-gaap_ScheduleOfGoodwillTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfGoodwillTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Goodwill [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfGoodwillTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfGoodwillTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfGoodwillTextBlock" xlink:to="lab_us-gaap_ScheduleOfGoodwillTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseNonoperating_fc05c29c-a3f1-467a-8981-6a4374063672_negatedLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseNonoperating" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Interest Expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseNonoperating_d33be709-a44f-40c0-a48f-2e9970e9e42f_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseNonoperating" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseNonoperating_label_en-US" xlink:label="lab_us-gaap_InterestExpenseNonoperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Nonoperating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseNonoperating" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseNonoperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseNonoperating" xlink:to="lab_us-gaap_InterestExpenseNonoperating" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TradingArrAxis_terseLabel_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Arrangement:</link:label>
    <link:label id="lab_ecd_TradingArrAxis_label_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TradingArrAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TradingArrAxis"/>
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    <link:label id="lab_ecd_TotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TotalShareholderRtnAmt"/>
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    <link:label id="lab_us-gaap_BusinessAcquisitionProFormaEarningsPerShareBasic_5e43210e-50f7-43e2-b673-baf992a31d82_verboseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionProFormaEarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Basic (in dollars per share)</link:label>
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    <link:label id="lab_us-gaap_CorporateNonSegmentMember_label_en-US" xlink:label="lab_us-gaap_CorporateNonSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Reconciling Item, Corporate Nonsegment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CorporateNonSegmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CorporateNonSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CorporateNonSegmentMember" xlink:to="lab_us-gaap_CorporateNonSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_SecurityExchangeName_10592a99-8a7b-42c3-bf81-9921efa10683_terseLabel_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
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    <link:label id="lab_kai_OperatingLeaseRightOfUseAssetNoncurrent_4f765365-f9e6-4bc1-a580-01cd42d55d04_terseLabel_en-US" xlink:label="lab_kai_OperatingLeaseRightOfUseAssetNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">ROU assets, non-current</link:label>
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    <link:label id="lab_us-gaap_IncomeTaxPaidForeignAfterRefundReceived_019bb2c1-6e26-7d7a-9aaf-fda7a237d9d7_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidForeignAfterRefundReceived" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign</link:label>
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    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationCrossBorderOtherPercent_019bb2ab-b494-7698-abbb-d73a709514d5_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationCrossBorderOtherPercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other, effect of cross-border tax laws</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationCrossBorderOtherPercent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationCrossBorderOtherPercent"/>
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    <link:label id="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpense_122a89e5-c55a-465a-a829-e6eb7e957a90_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nondeductible expenses</link:label>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpense_label_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationNondeductibleExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Nondeductible Expense, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReconciliationNondeductibleExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationNondeductibleExpense"/>
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    <link:label id="lab_us-gaap_CapitalExpendituresIncurredButNotYetPaid_b2fd414f-3e39-48be-95c9-315c73f02f7b_terseLabel_en-US" xlink:label="lab_us-gaap_CapitalExpendituresIncurredButNotYetPaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchases of property, plant and equipment in accounts payable</link:label>
    <link:label id="lab_us-gaap_CapitalExpendituresIncurredButNotYetPaid_label_en-US" xlink:label="lab_us-gaap_CapitalExpendituresIncurredButNotYetPaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Capital Expenditures Incurred but Not yet Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CapitalExpendituresIncurredButNotYetPaid" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CapitalExpendituresIncurredButNotYetPaid"/>
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    <link:label id="lab_us-gaap_OperatingExpensesAbstract_e4f0a06c-c96f-4e30-940d-cdfaf77a7500_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Expenses</link:label>
    <link:label id="lab_us-gaap_OperatingExpensesAbstract_label_en-US" xlink:label="lab_us-gaap_OperatingExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Expenses [Abstract]</link:label>
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    <link:label id="lab_us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain_5051600e-3f9c-4e17-b8a0-1926438c4dae_terseLabel_en-US" xlink:label="lab_us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Indefinite-lived Intangible Assets, Major Class Name [Domain]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IndefiniteLivedIntangibleAssetsMajorClassNameDomain"/>
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    <link:label id="lab_kai_TheClouthGroupOfCompaniesMember_79b0f70f-ccae-411d-a381-421c86f15cb8_terseLabel_en-US" xlink:label="lab_kai_TheClouthGroupOfCompaniesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">The Clouth Group of Companies</link:label>
    <link:label id="lab_kai_TheClouthGroupOfCompaniesMember_label_en-US" xlink:label="lab_kai_TheClouthGroupOfCompaniesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">The Clouth Group of Companies [Member]</link:label>
    <link:label id="lab_kai_TheClouthGroupOfCompaniesMember_documentation_en-US" xlink:label="lab_kai_TheClouthGroupOfCompaniesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The Clouth Group of Companies</link:label>
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    <link:label id="lab_us-gaap_OtherLiabilitiesCurrent_c4ad5396-717f-45fe-8d7f-10ed1ec8840b_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other current liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilitiesCurrent" xlink:to="lab_us-gaap_OtherLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementLineItems_11100231-fd21-4bf6-ba21-fa3172de17ff_terseLabel_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:label id="lab_us-gaap_StatementLineItems_label_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementLineItems" xlink:to="lab_us-gaap_StatementLineItems" xlink:type="arc" order="1"/>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:to="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_b8ab3fd5-59ee-49f7-8b83-79e028648316_verboseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_33ca76eb-1dd1-4e9d-9803-c23ae0469481_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalent</link:label>
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    <link:label id="lab_us-gaap_CommonStockMember_6c78dbfd-8587-4725-bd54-fbf7cafe9a35_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Stock</link:label>
    <link:label id="lab_us-gaap_CommonStockMember_label_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock [Member]</link:label>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod_f72cd480-7ea0-4344-932c-658fe57dd244_negatedLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Vested (in shares)</link:label>
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    <link:label id="lab_us-gaap_FinanceLeaseLiabilitiesPaymentsDueAbstract_aa5f392a-4848-4a51-96ab-72801e13060d_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilitiesPaymentsDueAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finance</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilitiesPaymentsDueAbstract_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilitiesPaymentsDueAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid, Fiscal Year Maturity [Abstract]</link:label>
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    <link:label id="lab_us-gaap_LeasesAbstract_387d7066-b8b3-4ded-bf2c-49a7e1e9e989_terseLabel_en-US" xlink:label="lab_us-gaap_LeasesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leases [Abstract]</link:label>
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    <link:label id="lab_kai_DeferredTaxAssetsInterestExpenseDisallowance_documentation_en-US" xlink:label="lab_kai_DeferredTaxAssetsInterestExpenseDisallowance" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Interest Expense Disallowance</link:label>
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    <link:label id="lab_ecd_TradingArrByIndTable_terseLabel_en-US" xlink:label="lab_ecd_TradingArrByIndTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Arrangements, by Individual</link:label>
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    <link:label id="lab_us-gaap_EarningsPerShareBasic_a5077e85-b3af-43d7-9623-1ea13f0140c4_verboseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Basic (in dollars per share)</link:label>
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    <link:label id="lab_us-gaap_LiabilitiesFairValueDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Fair Value Disclosure [Abstract]</link:label>
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    <link:label id="lab_us-gaap_CommonStockCapitalSharesReservedForFutureIssuance_4bb8f7dd-6206-4e15-99e5-11dd79047870_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock reserved and unissued (in shares)</link:label>
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    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTaxContingencies_019bb2ab-b494-7746-8f76-c4398870102d_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTaxContingencies" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changes in Unrecognized Tax Benefits</link:label>
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    <link:label id="lab_us-gaap_DeferredTaxAssetsGross_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsGross" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsGross"/>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax_2947b634-da37-437c-8f8a-af99c401cb92_totalLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Other Comprehensive Items</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax_b50f25c2-2aeb-4a06-a597-4a6dddfe7a03_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive items</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTax"/>
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    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_a071795e-560d-4e28-991c-e416eb3e6b8e_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Reportable Segments</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Segment Reporting Information, by Segment [Table Text Block]</link:label>
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    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligation_ed574651-5dcf-4b44-b58b-0a597adf9e66_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue, remaining performance obligation, amount</link:label>
    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligation_label_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue, Remaining Performance Obligation, Amount</link:label>
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    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree_785d6122-3603-4461-9ea5-d00fafd7e832_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid, Year Three</link:label>
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    <link:label id="lab_us-gaap_DeferredTaxAssetsTaxDeferredExpenseCompensationAndBenefits_248f00da-01b4-46dc-8f2b-c158bd94fd69_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsTaxDeferredExpenseCompensationAndBenefits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Employee compensation</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsTaxDeferredExpenseCompensationAndBenefits_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsTaxDeferredExpenseCompensationAndBenefits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Tax Deferred Expense, Compensation and Benefits</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsTaxDeferredExpenseCompensationAndBenefits" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsTaxDeferredExpenseCompensationAndBenefits"/>
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    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure</link:label>
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    <link:label id="lab_kai_RestructuringPlan2025Member_019b824e-c3d9-7b14-9433-de6c50447c0a_terseLabel_en-US" xlink:label="lab_kai_RestructuringPlan2025Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2025 Restructuring Plan</link:label>
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    <link:label id="lab_us-gaap_AllocatedShareBasedCompensationExpense_877d7a2d-91cf-4f50-be5f-88a4a32b3eeb_terseLabel_en-US" xlink:label="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock-based compensation expense</link:label>
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    <link:label id="lab_us-gaap_AssetsCurrentAbstract_1834254f-9b8e-49e3-9352-22459850a9ed_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current Assets:</link:label>
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    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Income Tax Liabilities, Net</link:label>
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    <link:label id="lab_us-gaap_DeferredTaxAssetsTaxCreditCarryforwardsForeign_2b9275ab-5e22-4ce8-8d60-7ef2b2f6d46d_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsTaxCreditCarryforwardsForeign" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign tax credits</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsTaxCreditCarryforwardsForeign_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsTaxCreditCarryforwardsForeign" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Tax Credit Carryforwards, Foreign</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsTaxCreditCarryforwardsForeign" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsTaxCreditCarryforwardsForeign"/>
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    <link:label id="lab_us-gaap_LongTermDebt_d1b16c9f-1fb0-4c4b-a312-d82a56d302ff_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term debt</link:label>
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    <link:label id="lab_us-gaap_Assets_2b9662b3-c380-4a1b-b03b-795a98daa88c_totalLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Assets</link:label>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_9aa98439-a447-43ec-8795-8d4bc80472bf_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
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    <link:label id="lab_us-gaap_IncomeTaxPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_IncomeTaxPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax, Policy [Policy Text Block]</link:label>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_a798cab9-502a-49da-93c2-8e384fe430e5_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Activities</link:label>
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    <link:label id="lab_us-gaap_BusinessExitCosts1_4fb86675-b4c6-4b73-96c0-a43969527d97_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessExitCosts1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Relocation costs</link:label>
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    <link:label id="lab_us-gaap_AssetsFairValueDisclosureAbstract_9f84ab49-a2da-4383-a80d-4da91173f5de_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets:</link:label>
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    <link:label id="lab_us-gaap_CommonStockDividendsPerShareDeclared_cf9292d0-2f93-4228-a67c-42285583c054_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockDividendsPerShareDeclared" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends declared - Common Stock (in dollars per share)</link:label>
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    <link:label id="lab_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_3de88f08-6182-45f6-9e66-ae8efe8bd746_terseLabel_en-US" xlink:label="lab_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating leases</link:label>
    <link:label id="lab_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_label_en-US" xlink:label="lab_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Right-of-Use Asset Obtained in Exchange for Operating Lease Liability</link:label>
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    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_3c4d3551-a413-46a6-abe8-b47320cc7ede_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 2</link:label>
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    <link:label id="lab_dei_DocumentFinStmtErrorCorrectionFlag_ac3b2a9b-caa9-4d33-af70-19ade51bee31_terseLabel_en-US" xlink:label="lab_dei_DocumentFinStmtErrorCorrectionFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Financial Statement Error Correction [Flag]</link:label>
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    <link:label id="lab_us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes_019bb2ab-b494-7693-907d-156e7242569e_verboseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">State and Local Income Tax, Net of Federal Income Tax Effect</link:label>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes_6613db43-9b37-4425-8e47-0e7575094f7b_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationStateAndLocalIncomeTaxes" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">State income taxes, net of federal income tax</link:label>
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    <link:label id="lab_kai_ContingentConsiderationLiabilityMember_3faaa4bd-da5a-4f09-b5b9-dda2c7fc6f77_terseLabel_en-US" xlink:label="lab_kai_ContingentConsiderationLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contingent Consideration Liability</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock"/>
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    <link:label id="lab_us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsAllowanceForDoubtfulAccounts_9095dd82-faeb-4960-bf6f-e3cb83ea6b37_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsAllowanceForDoubtfulAccounts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance for credit losses</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsAllowanceForDoubtfulAccounts_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsAllowanceForDoubtfulAccounts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Asset, Tax Deferred Expense, Reserve and Accrual, Accounts Receivable, Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsAllowanceForDoubtfulAccounts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsAllowanceForDoubtfulAccounts"/>
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    <link:label id="lab_us-gaap_NoncashOrPartNoncashAcquisitionValueOfAssetsAcquired1_66904179-4ddb-480e-b6ea-198ec73e6864_terseLabel_en-US" xlink:label="lab_us-gaap_NoncashOrPartNoncashAcquisitionValueOfAssetsAcquired1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value of assets acquired</link:label>
    <link:label id="lab_us-gaap_NoncashOrPartNoncashAcquisitionValueOfAssetsAcquired1_label_en-US" xlink:label="lab_us-gaap_NoncashOrPartNoncashAcquisitionValueOfAssetsAcquired1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncash or Part Noncash Acquisition, Value of Assets Acquired</link:label>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_ad98a427-1860-4201-bd22-2de848fdb891_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentPolicyTextBlock"/>
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    <link:label id="lab_ecd_PeoMember_terseLabel_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO</link:label>
    <link:label id="lab_ecd_PeoMember_label_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO [Member]</link:label>
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    <link:label id="lab_us-gaap_EmployeeSeveranceMember_0637aa98-e68d-418f-8cf2-abaaaf274dde_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeSeveranceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Severance Costs</link:label>
    <link:label id="lab_us-gaap_EmployeeSeveranceMember_label_en-US" xlink:label="lab_us-gaap_EmployeeSeveranceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Employee Severance [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeSeveranceMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EmployeeSeveranceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeSeveranceMember" xlink:to="lab_us-gaap_EmployeeSeveranceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_MachineryEquipmentAndLeaseholdImprovementsMember_21489c1c-4a87-40ca-a3bf-0ccc5e37dc69_terseLabel_en-US" xlink:label="lab_kai_MachineryEquipmentAndLeaseholdImprovementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Machinery, Equipment, and Leasehold Improvements</link:label>
    <link:label id="lab_kai_MachineryEquipmentAndLeaseholdImprovementsMember_label_en-US" xlink:label="lab_kai_MachineryEquipmentAndLeaseholdImprovementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Machinery, Equipment and Leasehold Improvements [Member]</link:label>
    <link:label id="lab_kai_MachineryEquipmentAndLeaseholdImprovementsMember_documentation_en-US" xlink:label="lab_kai_MachineryEquipmentAndLeaseholdImprovementsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Tangible personal property used to produce goods and services, including, but is not limited to, tools, dies and molds, computer and office equipment. This category also includes leasehold improvements.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_MachineryEquipmentAndLeaseholdImprovementsMember" xlink:href="kai-20260103.xsd#kai_MachineryEquipmentAndLeaseholdImprovementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_MachineryEquipmentAndLeaseholdImprovementsMember" xlink:to="lab_kai_MachineryEquipmentAndLeaseholdImprovementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentIncomeInterest_99dc0d57-6238-4b9c-8fd6-8c7d807a5989_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest Income</link:label>
    <link:label id="lab_us-gaap_InvestmentIncomeInterest_label_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Income, Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIncomeInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentIncomeInterest"/>
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    <link:label id="lab_us-gaap_IncomeTaxPaidByIndividualJurisdictionLineItems_019bb2c2-c1b0-7836-afa8-e457acc52b61_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidByIndividualJurisdictionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Paid, by Individual Jurisdiction [Line Items]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxPaidByIndividualJurisdictionLineItems_label_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidByIndividualJurisdictionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Paid, by Individual Jurisdiction [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxPaidByIndividualJurisdictionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxPaidByIndividualJurisdictionLineItems"/>
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    <link:label id="lab_country_US_742e6fc5-f204-496b-b697-0091818f8be4_terseLabel_en-US" xlink:label="lab_country_US" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">United States</link:label>
    <link:label id="lab_country_US_label_en-US" xlink:label="lab_country_US" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">UNITED STATES</link:label>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_228f6eb6-5ad7-464f-9ec6-2a38cbc02a9c_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changes in assets and liabilities, net of effects of acquisitions:</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity, Increase (Decrease) in Operating Capital [Abstract]</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfProductWarrantyLiabilityTableTextBlock_c7e686e0-5aad-48b7-add4-c0c61d373884_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfProductWarrantyLiabilityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changes in carrying amount of product warranty obligations</link:label>
    <link:label id="lab_us-gaap_ScheduleOfProductWarrantyLiabilityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfProductWarrantyLiabilityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Product Warranty Liability [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfProductWarrantyLiabilityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfProductWarrantyLiabilityTableTextBlock"/>
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    <link:label id="lab_us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance_22e1556d-dde8-45dd-8c00-8b06df433f5e_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in valuation allowance</link:label>
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    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment_ae48d5b9-e1f5-4ddf-b8aa-0d209c43e681_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Fixed asset basis difference</link:label>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment_label_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Property, Plant and Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment"/>
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    <link:label id="lab_us-gaap_RetainedEarningsMember_085d0981-ff3b-47af-8e35-aff2fef0f6d9_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Retained Earnings</link:label>
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    <link:label id="lab_us-gaap_IncomeTaxAuthorityAxis_549b86dc-fac9-4153-8a1b-c582490c139d_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Jurisdiction [Axis]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxAuthorityAxis_label_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Jurisdiction [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxAuthorityAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxAuthorityAxis"/>
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    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract_label_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement [Abstract]</link:label>
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    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_99e0b81e-fcab-457d-9cba-6197bf648901_periodStartLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalents, and Restricted Cash at Beginning of Year</link:label>
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    <link:label id="lab_us-gaap_IncomeStatementAbstract_2796c14e-a29c-43eb-9460-7aabf2992ec4_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Statement [Abstract]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Statement [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementAbstract" xlink:to="lab_us-gaap_IncomeStatementAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_PaymentToAcquireBusinessesOverdraft_c194da3b-bf31-4236-9f6d-18894eed49fc_terseLabel_en-US" xlink:label="lab_kai_PaymentToAcquireBusinessesOverdraft" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Overdraft</link:label>
    <link:label id="lab_kai_PaymentToAcquireBusinessesOverdraft_label_en-US" xlink:label="lab_kai_PaymentToAcquireBusinessesOverdraft" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment To Acquire Businesses, Overdraft</link:label>
    <link:label id="lab_kai_PaymentToAcquireBusinessesOverdraft_documentation_en-US" xlink:label="lab_kai_PaymentToAcquireBusinessesOverdraft" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Payment To Acquire Businesses, Overdraft</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_PaymentToAcquireBusinessesOverdraft" xlink:href="kai-20260103.xsd#kai_PaymentToAcquireBusinessesOverdraft"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_PaymentToAcquireBusinessesOverdraft" xlink:to="lab_kai_PaymentToAcquireBusinessesOverdraft" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StandardProductWarrantyAccrual_cf731d4c-080b-43fd-b201-a856d63f27a6_periodStartLabel_en-US" xlink:label="lab_us-gaap_StandardProductWarrantyAccrual" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Balance at Beginning of Year</link:label>
    <link:label id="lab_us-gaap_StandardProductWarrantyAccrual_9700a812-5342-49c4-aa4b-fcdb1968347e_periodEndLabel_en-US" xlink:label="lab_us-gaap_StandardProductWarrantyAccrual" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Balance at End of Year</link:label>
    <link:label id="lab_us-gaap_StandardProductWarrantyAccrual_label_en-US" xlink:label="lab_us-gaap_StandardProductWarrantyAccrual" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Standard Product Warranty Accrual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StandardProductWarrantyAccrual" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StandardProductWarrantyAccrual"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StandardProductWarrantyAccrual" xlink:to="lab_us-gaap_StandardProductWarrantyAccrual" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_ProceedsFromSaleOfPropertyPlantAndEquipmentMaximumPeriodForFullReceiptPeriodPostEffectiveDate_e755ce90-6a78-42d0-a98b-e602c87a8a92_terseLabel_en-US" xlink:label="lab_kai_ProceedsFromSaleOfPropertyPlantAndEquipmentMaximumPeriodForFullReceiptPeriodPostEffectiveDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Period of recognition of gain on sale and a receivable for remaining amount of sales proceeds (in years)</link:label>
    <link:label id="lab_kai_ProceedsFromSaleOfPropertyPlantAndEquipmentMaximumPeriodForFullReceiptPeriodPostEffectiveDate_label_en-US" xlink:label="lab_kai_ProceedsFromSaleOfPropertyPlantAndEquipmentMaximumPeriodForFullReceiptPeriodPostEffectiveDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds From Sale Of Property, Plant, And Equipment, Maximum Period For Full Receipt, Period Post Effective Date</link:label>
    <link:label id="lab_kai_ProceedsFromSaleOfPropertyPlantAndEquipmentMaximumPeriodForFullReceiptPeriodPostEffectiveDate_documentation_en-US" xlink:label="lab_kai_ProceedsFromSaleOfPropertyPlantAndEquipmentMaximumPeriodForFullReceiptPeriodPostEffectiveDate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Proceeds From Sale Of Property, Plant, And Equipment, Maximum Period For Full Receipt, Period Post Effective Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_ProceedsFromSaleOfPropertyPlantAndEquipmentMaximumPeriodForFullReceiptPeriodPostEffectiveDate" xlink:href="kai-20260103.xsd#kai_ProceedsFromSaleOfPropertyPlantAndEquipmentMaximumPeriodForFullReceiptPeriodPostEffectiveDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_ProceedsFromSaleOfPropertyPlantAndEquipmentMaximumPeriodForFullReceiptPeriodPostEffectiveDate" xlink:to="lab_kai_ProceedsFromSaleOfPropertyPlantAndEquipmentMaximumPeriodForFullReceiptPeriodPostEffectiveDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill_f842c9e0-9d31-4532-aa1e-7015f2d0905c_terseLabel_en-US" xlink:label="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible Assets, Net (Notes 1 and 2)</link:label>
    <link:label id="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill_c25efbae-2eae-4a43-8833-7cebf55ab540_totalLabel_en-US" xlink:label="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net</link:label>
    <link:label id="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill_label_en-US" xlink:label="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Assets, Net (Excluding Goodwill)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IntangibleAssetsNetExcludingGoodwill"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:to="lab_us-gaap_IntangibleAssetsNetExcludingGoodwill" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ProductsAndServicesDomain_beb34392-ee4e-4278-a609-c62130b7dfd7_terseLabel_en-US" xlink:label="lab_srt_ProductsAndServicesDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product and Service [Domain]</link:label>
    <link:label id="lab_srt_ProductsAndServicesDomain_label_en-US" xlink:label="lab_srt_ProductsAndServicesDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product and Service [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductsAndServicesDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProductsAndServicesDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ProductsAndServicesDomain" xlink:to="lab_srt_ProductsAndServicesDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProfitLoss_2298305b-a587-4b23-a0b1-5a9fe18ef030_totalLabel_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net Income</link:label>
    <link:label id="lab_us-gaap_ProfitLoss_05dd8eb3-55f7-4d0b-87eb-5619a445cc3e_terseLabel_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net income</link:label>
    <link:label id="lab_us-gaap_ProfitLoss_label_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss), Including Portion Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProfitLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProfitLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProfitLoss" xlink:to="lab_us-gaap_ProfitLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_terseLabel_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement does not require Recovery</link:label>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_label_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Does Not Require Recovery [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_RestatementDoesNotRequireRecoveryTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:to="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_ef1b80b8-d317-4da0-aaa1-bff100807637_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:to="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeNotionalAmount_29e067c0-5f63-411c-ac88-b8fa20b6734a_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Notional amount</link:label>
    <link:label id="lab_us-gaap_DerivativeNotionalAmount_label_en-US" xlink:label="lab_us-gaap_DerivativeNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Notional Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeNotionalAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeNotionalAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeNotionalAmount" xlink:to="lab_us-gaap_DerivativeNotionalAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeDefinedBenefitPlansNetUnamortizedGainLossArisingDuringPeriodNetOfTax_3cd7524a-cb61-4d09-b072-b7a919a8df7f_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeDefinedBenefitPlansNetUnamortizedGainLossArisingDuringPeriodNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension and other post-retirement liability adjustments, net (net of tax (benefit) provision of $(7), $17, and $45)</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeDefinedBenefitPlansNetUnamortizedGainLossArisingDuringPeriodNetOfTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeDefinedBenefitPlansNetUnamortizedGainLossArisingDuringPeriodNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Defined Benefit Plan, Gain (Loss) Arising During Period, after Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeDefinedBenefitPlansNetUnamortizedGainLossArisingDuringPeriodNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeDefinedBenefitPlansNetUnamortizedGainLossArisingDuringPeriodNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeDefinedBenefitPlansNetUnamortizedGainLossArisingDuringPeriodNetOfTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeDefinedBenefitPlansNetUnamortizedGainLossArisingDuringPeriodNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxPaidByIndividualJurisdictionTable_019bb2c2-867b-7993-96c5-e812b79b4ede_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidByIndividualJurisdictionTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Paid, by Individual Jurisdiction [Table]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxPaidByIndividualJurisdictionTable_label_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidByIndividualJurisdictionTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Paid, by Individual Jurisdiction [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxPaidByIndividualJurisdictionTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxPaidByIndividualJurisdictionTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxPaidByIndividualJurisdictionTable" xlink:to="lab_us-gaap_IncomeTaxPaidByIndividualJurisdictionTable" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_SegmentOperatingIncomeMarginPercent_306e31d7-acad-46da-9246-891e97d096f9_terseLabel_en-US" xlink:label="lab_kai_SegmentOperatingIncomeMarginPercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Operating Income Margin</link:label>
    <link:label id="lab_kai_SegmentOperatingIncomeMarginPercent_label_en-US" xlink:label="lab_kai_SegmentOperatingIncomeMarginPercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Operating Income Margin, Percent</link:label>
    <link:label id="lab_kai_SegmentOperatingIncomeMarginPercent_documentation_en-US" xlink:label="lab_kai_SegmentOperatingIncomeMarginPercent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Segment Operating Income Margin, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_SegmentOperatingIncomeMarginPercent" xlink:href="kai-20260103.xsd#kai_SegmentOperatingIncomeMarginPercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_SegmentOperatingIncomeMarginPercent" xlink:to="lab_kai_SegmentOperatingIncomeMarginPercent" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CityAreaCode_f0e5e807-6922-4a29-a78d-9610560baf50_terseLabel_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:label id="lab_dei_CityAreaCode_label_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CityAreaCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CityAreaCode" xlink:to="lab_dei_CityAreaCode" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardTmgHowMnpiCnsdrdTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:to="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock_34f4f174-9047-44dd-8575-b9954795f438_terseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contract balances from contracts with customers</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract with Customer, Contract Asset, Contract Liability, and Receivable [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock" xlink:to="lab_us-gaap_ContractWithCustomerAssetAndLiabilityTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxLiabilities_e98930d3-406f-4ff3-9920-9b4047902ef4_negatedTotalLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilities" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Net deferred tax liability</link:label>
    <link:label id="lab_us-gaap_DeferredTaxLiabilities_label_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxLiabilities" xlink:to="lab_us-gaap_DeferredTaxLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_6be0fb42-df9b-4ff5-b37b-3cbbd2214d89_terseLabel_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">General and administrative expenses</link:label>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_1dbaf260-cf75-4ccc-8182-fdbbc1046822_negatedLabel_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">General and administrative expenses</link:label>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_label_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">General and Administrative Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GeneralAndAdministrativeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GeneralAndAdministrativeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GeneralAndAdministrativeExpense" xlink:to="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_4ea58b29-f0e8-4073-96cc-1c98168069af_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investing Activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PvpTable_terseLabel_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure</link:label>
    <link:label id="lab_ecd_PvpTable_label_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTable" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PvpTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PvpTable" xlink:to="lab_ecd_PvpTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeaseCost_1f3d68e6-ae45-40f6-817d-325acb4d2990_totalLabel_en-US" xlink:label="lab_us-gaap_LeaseCost" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Lease Costs</link:label>
    <link:label id="lab_us-gaap_LeaseCost_label_en-US" xlink:label="lab_us-gaap_LeaseCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeaseCost" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LeaseCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeaseCost" xlink:to="lab_us-gaap_LeaseCost" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_LeaseOptiontoExtendTerm_12829a56-0b8e-4fd7-8590-89400172b996_terseLabel_en-US" xlink:label="lab_kai_LeaseOptiontoExtendTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lease, option to extend, term</link:label>
    <link:label id="lab_kai_LeaseOptiontoExtendTerm_label_en-US" xlink:label="lab_kai_LeaseOptiontoExtendTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease, Option to Extend, Term</link:label>
    <link:label id="lab_kai_LeaseOptiontoExtendTerm_documentation_en-US" xlink:label="lab_kai_LeaseOptiontoExtendTerm" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lease, Option to Extend, Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_LeaseOptiontoExtendTerm" xlink:href="kai-20260103.xsd#kai_LeaseOptiontoExtendTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_LeaseOptiontoExtendTerm" xlink:to="lab_kai_LeaseOptiontoExtendTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationLineItems_019bb2ab-b494-7bae-a580-ce91c436cd8d_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation [Line Items]</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationLineItems_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectiveIncomeTaxRateReconciliationLineItems" xlink:to="lab_us-gaap_EffectiveIncomeTaxRateReconciliationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SellingGeneralAndAdministrativeExpensesMember_b34956a0-15a6-4b2e-8bc3-9f17a4a5185b_terseLabel_en-US" xlink:label="lab_us-gaap_SellingGeneralAndAdministrativeExpensesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Selling, general and administrative expenses</link:label>
    <link:label id="lab_us-gaap_SellingGeneralAndAdministrativeExpensesMember_label_en-US" xlink:label="lab_us-gaap_SellingGeneralAndAdministrativeExpensesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Selling, General and Administrative Expenses [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SellingGeneralAndAdministrativeExpensesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SellingGeneralAndAdministrativeExpensesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SellingGeneralAndAdministrativeExpensesMember" xlink:to="lab_us-gaap_SellingGeneralAndAdministrativeExpensesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Goodwill_b8c44e39-9c36-416c-b219-17850bf2b25e_terseLabel_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill (Notes 1 and 2)</link:label>
    <link:label id="lab_us-gaap_Goodwill_e2f26414-acb6-4204-b35b-7ae38c6766af_periodStartLabel_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Net balance, beginning balance</link:label>
    <link:label id="lab_us-gaap_Goodwill_4a0f439b-6283-4f49-b6b4-ad303ee35072_periodEndLabel_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Net balance, ending balance</link:label>
    <link:label id="lab_us-gaap_Goodwill_0f1c60f1-43b1-4ede-989a-d44b175d0dd1_totalLabel_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net balance</link:label>
    <link:label id="lab_us-gaap_Goodwill_ecb6081a-6f18-4e84-8411-02df291119f1_verboseLabel_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:label id="lab_us-gaap_Goodwill_label_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Goodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Goodwill"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Goodwill" xlink:to="lab_us-gaap_Goodwill" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LeaseCostTableTextBlock_1809afca-2042-4fda-84fd-55322a74777d_terseLabel_en-US" xlink:label="lab_us-gaap_LeaseCostTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Components of lease expense</link:label>
    <link:label id="lab_us-gaap_LeaseCostTableTextBlock_label_en-US" xlink:label="lab_us-gaap_LeaseCostTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease, Cost [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeaseCostTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LeaseCostTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeaseCostTableTextBlock" xlink:to="lab_us-gaap_LeaseCostTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_MaximumConsolidatedLeverageRatio_0d1ed8ef-931b-446b-8d01-e31592ed0221_terseLabel_en-US" xlink:label="lab_kai_MaximumConsolidatedLeverageRatio" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum consolidated leverage ratio</link:label>
    <link:label id="lab_kai_MaximumConsolidatedLeverageRatio_label_en-US" xlink:label="lab_kai_MaximumConsolidatedLeverageRatio" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maximum Consolidated Leverage Ratio</link:label>
    <link:label id="lab_kai_MaximumConsolidatedLeverageRatio_documentation_en-US" xlink:label="lab_kai_MaximumConsolidatedLeverageRatio" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The maximum consolidated leverage ratio under the negative covenants of the credit facility.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_MaximumConsolidatedLeverageRatio" xlink:href="kai-20260103.xsd#kai_MaximumConsolidatedLeverageRatio"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_MaximumConsolidatedLeverageRatio" xlink:to="lab_kai_MaximumConsolidatedLeverageRatio" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredFederalIncomeTaxExpenseBenefit_12574205-2905-4836-933f-9e82f71b7c71_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredFederalIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Federal</link:label>
    <link:label id="lab_us-gaap_DeferredFederalIncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_DeferredFederalIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Federal Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredFederalIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredFederalIncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredFederalIncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_DeferredFederalIncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReconciliationOfUnrecognizedTaxBenefitsExcludingAmountsPertainingToExaminedTaxReturnsRollForward_918677e2-c9de-4140-bf38-2053f3dd4715_terseLabel_en-US" xlink:label="lab_us-gaap_ReconciliationOfUnrecognizedTaxBenefitsExcludingAmountsPertainingToExaminedTaxReturnsRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reconciliation of Unrecognized Tax Benefits [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_ReconciliationOfUnrecognizedTaxBenefitsExcludingAmountsPertainingToExaminedTaxReturnsRollForward_label_en-US" xlink:label="lab_us-gaap_ReconciliationOfUnrecognizedTaxBenefitsExcludingAmountsPertainingToExaminedTaxReturnsRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrecognized Tax Benefits [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReconciliationOfUnrecognizedTaxBenefitsExcludingAmountsPertainingToExaminedTaxReturnsRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReconciliationOfUnrecognizedTaxBenefitsExcludingAmountsPertainingToExaminedTaxReturnsRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReconciliationOfUnrecognizedTaxBenefitsExcludingAmountsPertainingToExaminedTaxReturnsRollForward" xlink:to="lab_us-gaap_ReconciliationOfUnrecognizedTaxBenefitsExcludingAmountsPertainingToExaminedTaxReturnsRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AuditorName_41609d13-9601-4629-a2ff-f578f2a2a190_terseLabel_en-US" xlink:label="lab_dei_AuditorName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Auditor Name</link:label>
    <link:label id="lab_dei_AuditorName_label_en-US" xlink:label="lab_dei_AuditorName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Auditor Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AuditorName" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_AuditorName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_AuditorName" xlink:to="lab_dei_AuditorName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedInventory_26794a42-2234-44c4-b04c-74d00185a2c2_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedInventory" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Inventories</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedInventory_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedInventory" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Inventory, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedInventory" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedInventory"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedInventory" xlink:to="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedInventory" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_GrossProfitMarginPercent_4fb48bf0-867e-4376-9f3d-85a2993e4c75_terseLabel_en-US" xlink:label="lab_kai_GrossProfitMarginPercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross Profit Margin</link:label>
    <link:label id="lab_kai_GrossProfitMarginPercent_label_en-US" xlink:label="lab_kai_GrossProfitMarginPercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gross Profit Margin, Percent</link:label>
    <link:label id="lab_kai_GrossProfitMarginPercent_documentation_en-US" xlink:label="lab_kai_GrossProfitMarginPercent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Gross Profit Margin, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_GrossProfitMarginPercent" xlink:href="kai-20260103.xsd#kai_GrossProfitMarginPercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_GrossProfitMarginPercent" xlink:to="lab_kai_GrossProfitMarginPercent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables_2b867314-f282-4d2a-8150-a0cb29be9d6d_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts Receivable</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Receivable, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables" xlink:to="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestructuringCostAndReserveLineItems_619ea238-f125-4083-9aef-ba1b68433138_terseLabel_en-US" xlink:label="lab_us-gaap_RestructuringCostAndReserveLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restructuring Cost and Reserve [Line Items]</link:label>
    <link:label id="lab_us-gaap_RestructuringCostAndReserveLineItems_label_en-US" xlink:label="lab_us-gaap_RestructuringCostAndReserveLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restructuring Cost and Reserve [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestructuringCostAndReserveLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestructuringCostAndReserveLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestructuringCostAndReserveLineItems" xlink:to="lab_us-gaap_RestructuringCostAndReserveLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss_0146beb4-0ac8-41cc-ac16-0231379c656b_negatedPeriodStartLabel_en-US" xlink:label="lab_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss" xlink:role="http://www.xbrl.org/2009/role/negatedPeriodStartLabel" xlink:type="resource" xml:lang="en-US">Accumulated impairment losses</link:label>
    <link:label id="lab_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss_9da7517a-ab4d-4892-9194-67b896b59cbd_negatedPeriodEndLabel_en-US" xlink:label="lab_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss" xlink:role="http://www.xbrl.org/2009/role/negatedPeriodEndLabel" xlink:type="resource" xml:lang="en-US">Accumulated impairment losses</link:label>
    <link:label id="lab_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss_23a6765e-055b-47fc-8443-2cc78e8f2afd_negatedLabel_en-US" xlink:label="lab_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Accumulated impairment losses</link:label>
    <link:label id="lab_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss_label_en-US" xlink:label="lab_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill, Impaired, Accumulated Impairment Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillImpairedAccumulatedImpairmentLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss" xlink:to="lab_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_label_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OtherPerfMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_OtherPerfMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OtherPerfMeasureAmt" xlink:to="lab_ecd_OtherPerfMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock_0b68b4da-70b2-4f7c-9f95-5325c2b29b7c_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reconciliation of restricted cash</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restrictions on Cash and Cash Equivalents [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock" xlink:to="lab_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationGainLossArisingDuringPeriodNetOfTax_1e58b4a6-a443-4e93-9a60-44bb27f2338d_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationGainLossArisingDuringPeriodNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign currency translation adjustment</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationGainLossArisingDuringPeriodNetOfTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationGainLossArisingDuringPeriodNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Foreign Currency Transaction and Translation Gain (Loss) Arising During Period, Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationGainLossArisingDuringPeriodNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationGainLossArisingDuringPeriodNetOfTax"/>
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    <link:label id="lab_us-gaap_DebtCurrent_482fa445-fb7e-4f64-a0d2-320bcf6043af_terseLabel_en-US" xlink:label="lab_us-gaap_DebtCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current maturities of long-term obligations (Note 6)</link:label>
    <link:label id="lab_us-gaap_DebtCurrent_a21dcc24-0531-4af6-a25a-5c4b86ecfd8e_negatedLabel_en-US" xlink:label="lab_us-gaap_DebtCurrent" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Less: Current Maturities of Long-Term Obligations</link:label>
    <link:label id="lab_us-gaap_DebtCurrent_label_en-US" xlink:label="lab_us-gaap_DebtCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtCurrent" xlink:to="lab_us-gaap_DebtCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementPolicyPolicyTextBlock_c435de1f-0355-4a03-ba5a-7ee569939484_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurement</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:to="lab_us-gaap_FairValueMeasurementPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PensionAndOtherPostretirementPlansPolicy_b0c3f228-0feb-4422-aca8-ae9321037f4e_terseLabel_en-US" xlink:label="lab_us-gaap_PensionAndOtherPostretirementPlansPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension and Other Post-Retirement Defined Benefits Plans</link:label>
    <link:label id="lab_us-gaap_PensionAndOtherPostretirementPlansPolicy_label_en-US" xlink:label="lab_us-gaap_PensionAndOtherPostretirementPlansPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension and Other Postretirement Plans, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PensionAndOtherPostretirementPlansPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PensionAndOtherPostretirementPlansPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PensionAndOtherPostretirementPlansPolicy" xlink:to="lab_us-gaap_PensionAndOtherPostretirementPlansPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Dividends_972afe22-6557-4682-b94d-962bff9db84c_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_Dividends" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Dividends declared - Common Stock</link:label>
    <link:label id="lab_us-gaap_Dividends_label_en-US" xlink:label="lab_us-gaap_Dividends" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Dividends" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Dividends"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Dividends" xlink:to="lab_us-gaap_Dividends" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract_019bb2ab-b494-77b3-9884-4a10ec37b5c5_verboseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Amount</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Expense (Benefit), Effective Income Tax Rate Reconciliation, Amount [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract" xlink:to="lab_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_4b38a690-bcad-4f1c-a5d5-f11f512e8709_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentRiskAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeInstrumentRiskAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentRiskAxis" xlink:to="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeFinanceLeasesTextBlock_47e627b3-0483-4a44-af61-4eae7286f69b_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeFinanceLeasesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leases</link:label>
    <link:label id="lab_us-gaap_LesseeFinanceLeasesTextBlock_label_en-US" xlink:label="lab_us-gaap_LesseeFinanceLeasesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Finance Leases [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeFinanceLeasesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeFinanceLeasesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeFinanceLeasesTextBlock" xlink:to="lab_us-gaap_LesseeFinanceLeasesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_PerformanceBasedRestrictedStockUnitsMember_44d54abe-223c-4e03-9da7-cd2215f03821_terseLabel_en-US" xlink:label="lab_kai_PerformanceBasedRestrictedStockUnitsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Performance-based restricted stock units</link:label>
    <link:label id="lab_kai_PerformanceBasedRestrictedStockUnitsMember_label_en-US" xlink:label="lab_kai_PerformanceBasedRestrictedStockUnitsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Performance Based Restricted Stock Units [Member]</link:label>
    <link:label id="lab_kai_PerformanceBasedRestrictedStockUnitsMember_documentation_en-US" xlink:label="lab_kai_PerformanceBasedRestrictedStockUnitsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Performance Based Restricted Stock Units [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_PerformanceBasedRestrictedStockUnitsMember" xlink:href="kai-20260103.xsd#kai_PerformanceBasedRestrictedStockUnitsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_PerformanceBasedRestrictedStockUnitsMember" xlink:to="lab_kai_PerformanceBasedRestrictedStockUnitsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAssetsCurrent_fe64886f-27cc-4d01-8dcb-55fb70432c78_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other current assets</link:label>
    <link:label id="lab_us-gaap_OtherAssetsCurrent_label_en-US" xlink:label="lab_us-gaap_OtherAssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssetsCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherAssetsCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssetsCurrent" xlink:to="lab_us-gaap_OtherAssetsCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_OperatingLeasesAbstract_38aee640-12f2-4c67-abfc-1e9d12b590e2_terseLabel_en-US" xlink:label="lab_kai_OperatingLeasesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Leases:</link:label>
    <link:label id="lab_kai_OperatingLeasesAbstract_label_en-US" xlink:label="lab_kai_OperatingLeasesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Leases [Abstract]</link:label>
    <link:label id="lab_kai_OperatingLeasesAbstract_documentation_en-US" xlink:label="lab_kai_OperatingLeasesAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Operating Leases [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_OperatingLeasesAbstract" xlink:href="kai-20260103.xsd#kai_OperatingLeasesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_OperatingLeasesAbstract" xlink:to="lab_kai_OperatingLeasesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_3438209b-2104-4946-bd76-11a0325b590f_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash used in investing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities"/>
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    <link:label id="lab_kai_FluidHandlingMember_c50861ba-fb66-4c05-99b9-7d00291f06a6_terseLabel_en-US" xlink:label="lab_kai_FluidHandlingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fluid-Handling</link:label>
    <link:label id="lab_kai_FluidHandlingMember_label_en-US" xlink:label="lab_kai_FluidHandlingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fluid handling [Member]</link:label>
    <link:label id="lab_kai_FluidHandlingMember_documentation_en-US" xlink:label="lab_kai_FluidHandlingMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Operating segment product line.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_FluidHandlingMember" xlink:href="kai-20260103.xsd#kai_FluidHandlingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_FluidHandlingMember" xlink:to="lab_kai_FluidHandlingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1_29e6517d-5f3c-4f2a-b672-0a581f1cdf5e_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue, remaining performance obligation, expected timing of satisfaction after the twelve month period</link:label>
    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1_label_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction, Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1"/>
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    <link:label id="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Change in Present Value of Accumulated Benefit for All Pension Plans Reported in Summary Compensation Table</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:to="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestPaidNet_2a8fd951-9800-4a1c-8897-30a1d3c5c688_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash Paid for Interest</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_kai_PreferredStockAbstract" xlink:href="kai-20260103.xsd#kai_PreferredStockAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_PreferredStockAbstract" xlink:to="lab_kai_PreferredStockAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_IncreaseDecreaseInContractWithCustomerLiabilityCustomerDeposits_c42b1c41-e044-47c8-b121-96a3ca31d82f_terseLabel_en-US" xlink:label="lab_kai_IncreaseDecreaseInContractWithCustomerLiabilityCustomerDeposits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Customer deposits</link:label>
    <link:label id="lab_kai_IncreaseDecreaseInContractWithCustomerLiabilityCustomerDeposits_label_en-US" xlink:label="lab_kai_IncreaseDecreaseInContractWithCustomerLiabilityCustomerDeposits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Contract with Customer, Liability, Customer Deposits</link:label>
    <link:label id="lab_kai_IncreaseDecreaseInContractWithCustomerLiabilityCustomerDeposits_documentation_en-US" xlink:label="lab_kai_IncreaseDecreaseInContractWithCustomerLiabilityCustomerDeposits" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Contract with Customer, Liability, Customer Deposits</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_IncreaseDecreaseInContractWithCustomerLiabilityCustomerDeposits" xlink:href="kai-20260103.xsd#kai_IncreaseDecreaseInContractWithCustomerLiabilityCustomerDeposits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_IncreaseDecreaseInContractWithCustomerLiabilityCustomerDeposits" xlink:to="lab_kai_IncreaseDecreaseInContractWithCustomerLiabilityCustomerDeposits" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiability_41c00b19-9793-444c-acf5-bc8719e7e8cc_verboseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Finance Leases, due 2026 to 2029</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiability_07b77e2e-dd5c-4620-826e-766b86d0b3ac_totalLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total finance lease liabilities</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiability_67491bcf-917a-44c3-b3c9-11f21156cade_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Present Value of Lease Payments</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiability_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiability" xlink:to="lab_us-gaap_FinanceLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrDuration_terseLabel_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Arrangement Duration</link:label>
    <link:label id="lab_ecd_TrdArrDuration_label_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Duration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrDuration" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrDuration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrDuration" xlink:to="lab_ecd_TrdArrDuration" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual_027d4d93-ad02-4f8e-b61a-552fc20920b5_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Income</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Acquiree's Earnings (Loss) since Acquisition Date, Actual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual" xlink:to="lab_us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_InterestExpenseNonoperatingNet_35e9d5b6-baa9-4154-a2a2-d113bedcd119_negatedTerseLabel_en-US" xlink:label="lab_kai_InterestExpenseNonoperatingNet" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Interest Expense, Net</link:label>
    <link:label id="lab_kai_InterestExpenseNonoperatingNet_label_en-US" xlink:label="lab_kai_InterestExpenseNonoperatingNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Nonoperating, Net</link:label>
    <link:label id="lab_kai_InterestExpenseNonoperatingNet_documentation_en-US" xlink:label="lab_kai_InterestExpenseNonoperatingNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest Expense, Nonoperating, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_InterestExpenseNonoperatingNet" xlink:href="kai-20260103.xsd#kai_InterestExpenseNonoperatingNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_InterestExpenseNonoperatingNet" xlink:to="lab_kai_InterestExpenseNonoperatingNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_d4e35d0b-dea6-42e4-952f-33aa103d8afe_terseLabel_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segments [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segments [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementBusinessSegmentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:to="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_IndemnificationAssetAmount_d04926bb-d7c6-4084-a65a-77fc644b2d30_terseLabel_en-US" xlink:label="lab_kai_IndemnificationAssetAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Indemnification assets</link:label>
    <link:label id="lab_kai_IndemnificationAssetAmount_label_en-US" xlink:label="lab_kai_IndemnificationAssetAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Indemnification Asset, Amount</link:label>
    <link:label id="lab_kai_IndemnificationAssetAmount_documentation_en-US" xlink:label="lab_kai_IndemnificationAssetAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Indemnification Asset, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_IndemnificationAssetAmount" xlink:href="kai-20260103.xsd#kai_IndemnificationAssetAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_IndemnificationAssetAmount" xlink:to="lab_kai_IndemnificationAssetAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain_98d15710-a75e-4ac7-8a4b-1fe67e3f9723_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value by Liability Class [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain_label_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value by Liability Class [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:to="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LocalPhoneNumber_e4e01e59-2a96-4489-a9ea-7b7fde760ac0_terseLabel_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:label id="lab_dei_LocalPhoneNumber_label_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_LocalPhoneNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LocalPhoneNumber" xlink:to="lab_dei_LocalPhoneNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Additional402vDisclosureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_Additional402vDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional 402(v) Disclosure</link:label>
    <link:label id="lab_ecd_Additional402vDisclosureTextBlock_label_en-US" xlink:label="lab_ecd_Additional402vDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional 402(v) Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Additional402vDisclosureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_Additional402vDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Additional402vDisclosureTextBlock" xlink:to="lab_ecd_Additional402vDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_EighthAmendmentToUnsecuredMultiCurrencyRevolvingCreditFacilityCreditAgreementMember_019b8243-c105-73db-a089-cb28d7dfdb8c_terseLabel_en-US" xlink:label="lab_kai_EighthAmendmentToUnsecuredMultiCurrencyRevolvingCreditFacilityCreditAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Eighth Amendment To Unsecured Multi-Currency Revolving Credit Facility ("Credit Agreement")</link:label>
    <link:label id="lab_kai_EighthAmendmentToUnsecuredMultiCurrencyRevolvingCreditFacilityCreditAgreementMember_label_en-US" xlink:label="lab_kai_EighthAmendmentToUnsecuredMultiCurrencyRevolvingCreditFacilityCreditAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Eighth Amendment To Unsecured Multi-Currency Revolving Credit Facility ("Credit Agreement") [Member]</link:label>
    <link:label id="lab_kai_EighthAmendmentToUnsecuredMultiCurrencyRevolvingCreditFacilityCreditAgreementMember_documentation_en-US" xlink:label="lab_kai_EighthAmendmentToUnsecuredMultiCurrencyRevolvingCreditFacilityCreditAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Eighth Amendment To Unsecured Multi-Currency Revolving Credit Facility ("Credit Agreement")</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_EighthAmendmentToUnsecuredMultiCurrencyRevolvingCreditFacilityCreditAgreementMember" xlink:href="kai-20260103.xsd#kai_EighthAmendmentToUnsecuredMultiCurrencyRevolvingCreditFacilityCreditAgreementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_EighthAmendmentToUnsecuredMultiCurrencyRevolvingCreditFacilityCreditAgreementMember" xlink:to="lab_kai_EighthAmendmentToUnsecuredMultiCurrencyRevolvingCreditFacilityCreditAgreementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_EuropeMember_f9ddea78-9386-4298-9bec-919d642a78e9_terseLabel_en-US" xlink:label="lab_srt_EuropeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Europe</link:label>
    <link:label id="lab_srt_EuropeMember_label_en-US" xlink:label="lab_srt_EuropeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Europe [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_EuropeMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_EuropeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_EuropeMember" xlink:to="lab_srt_EuropeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities_0ecdb8ae-f02c-4ffd-8d9b-051b22e59183_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Other investing activities</link:label>
    <link:label id="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities_label_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment for (Proceeds from) Other Investing Activity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsForProceedsFromOtherInvestingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:to="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive_c8751b44-31be-4ef7-b4f7-3d84b8df2208_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2031</link:label>
    <link:label id="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive_label_en-US" xlink:label="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Maturity, after Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:to="lab_us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_OtherOperatingIncomeNet_019caf31-8fcc-7920-81eb-e6fea790b04d_verboseLabel_en-US" xlink:label="lab_kai_OtherOperatingIncomeNet" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other costs, net (Note 8)</link:label>
    <link:label id="lab_kai_OtherOperatingIncomeNet_019caf31-f9fd-703b-b274-1529794ba51b_totalLabel_en-US" xlink:label="lab_kai_OtherOperatingIncomeNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Other costs, net</link:label>
    <link:label id="lab_kai_OtherOperatingIncomeNet_label_en-US" xlink:label="lab_kai_OtherOperatingIncomeNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Operating Income, Net</link:label>
    <link:label id="lab_kai_OtherOperatingIncomeNet_documentation_en-US" xlink:label="lab_kai_OtherOperatingIncomeNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Operating Income, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_OtherOperatingIncomeNet" xlink:href="kai-20260103.xsd#kai_OtherOperatingIncomeNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_OtherOperatingIncomeNet" xlink:to="lab_kai_OtherOperatingIncomeNet" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_MaximumConsolidatedLeverageRatioUponMaterialAcquisition_f39d1011-0e13-4802-9d54-4d440c9cfef8_terseLabel_en-US" xlink:label="lab_kai_MaximumConsolidatedLeverageRatioUponMaterialAcquisition" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum consolidated leverage ratio upon material acquisition</link:label>
    <link:label id="lab_kai_MaximumConsolidatedLeverageRatioUponMaterialAcquisition_label_en-US" xlink:label="lab_kai_MaximumConsolidatedLeverageRatioUponMaterialAcquisition" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maximum Consolidated Leverage Ratio Upon Material Acquisition</link:label>
    <link:label id="lab_kai_MaximumConsolidatedLeverageRatioUponMaterialAcquisition_documentation_en-US" xlink:label="lab_kai_MaximumConsolidatedLeverageRatioUponMaterialAcquisition" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Maximum Consolidated Leverage Ratio Upon Material Acquisition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_MaximumConsolidatedLeverageRatioUponMaterialAcquisition" xlink:href="kai-20260103.xsd#kai_MaximumConsolidatedLeverageRatioUponMaterialAcquisition"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_MaximumConsolidatedLeverageRatioUponMaterialAcquisition" xlink:to="lab_kai_MaximumConsolidatedLeverageRatioUponMaterialAcquisition" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill_4b65c255-f1a0-4e9b-bc85-5e032350a5fd_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible assets other than goodwill acquired</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Identifiable Intangible Asset, Excluding Goodwill</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLiabilityNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:to="lab_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityVoluntaryFilers_8267a9cf-35e6-468b-8676-4e94dc1d98bf_terseLabel_en-US" xlink:label="lab_dei_EntityVoluntaryFilers" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Voluntary Filers</link:label>
    <link:label id="lab_dei_EntityVoluntaryFilers_label_en-US" xlink:label="lab_dei_EntityVoluntaryFilers" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Voluntary Filers</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityVoluntaryFilers" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityVoluntaryFilers"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityVoluntaryFilers" xlink:to="lab_dei_EntityVoluntaryFilers" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IntangibleAssetsNetExcludingGoodwillAbstract_2dd04f86-a51e-481f-b999-2656ba0bb0b5_terseLabel_en-US" xlink:label="lab_us-gaap_IntangibleAssetsNetExcludingGoodwillAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquired Intangible Assets</link:label>
    <link:label id="lab_us-gaap_IntangibleAssetsNetExcludingGoodwillAbstract_label_en-US" xlink:label="lab_us-gaap_IntangibleAssetsNetExcludingGoodwillAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Assets, Net (Excluding Goodwill) [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IntangibleAssetsNetExcludingGoodwillAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IntangibleAssetsNetExcludingGoodwillAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IntangibleAssetsNetExcludingGoodwillAbstract" xlink:to="lab_us-gaap_IntangibleAssetsNetExcludingGoodwillAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_RestrictedStockUnitsForNonEmployeeDirectorsRsusMember_2489ed22-dc0e-48e4-9786-15529bf2779e_terseLabel_en-US" xlink:label="lab_kai_RestrictedStockUnitsForNonEmployeeDirectorsRsusMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted stock units for non employee directors (RSUs)</link:label>
    <link:label id="lab_kai_RestrictedStockUnitsForNonEmployeeDirectorsRsusMember_label_en-US" xlink:label="lab_kai_RestrictedStockUnitsForNonEmployeeDirectorsRsusMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Stock Units for Non Employee Directors (RSUs) [Member]</link:label>
    <link:label id="lab_kai_RestrictedStockUnitsForNonEmployeeDirectorsRsusMember_documentation_en-US" xlink:label="lab_kai_RestrictedStockUnitsForNonEmployeeDirectorsRsusMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Stock units that an entity has not yet issued because the agreed-upon consideration, such as employee services, has not yet been received.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_RestrictedStockUnitsForNonEmployeeDirectorsRsusMember" xlink:href="kai-20260103.xsd#kai_RestrictedStockUnitsForNonEmployeeDirectorsRsusMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_RestrictedStockUnitsForNonEmployeeDirectorsRsusMember" xlink:to="lab_kai_RestrictedStockUnitsForNonEmployeeDirectorsRsusMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_ContractWithCustomerLiabilityCurrentCustomerDeposits_5de168d1-ca48-4153-8f03-d3ec02c0a93c_terseLabel_en-US" xlink:label="lab_kai_ContractWithCustomerLiabilityCurrentCustomerDeposits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Customer deposits</link:label>
    <link:label id="lab_kai_ContractWithCustomerLiabilityCurrentCustomerDeposits_label_en-US" xlink:label="lab_kai_ContractWithCustomerLiabilityCurrentCustomerDeposits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract With Customer, Liability, Current, Customer Deposits</link:label>
    <link:label id="lab_kai_ContractWithCustomerLiabilityCurrentCustomerDeposits_documentation_en-US" xlink:label="lab_kai_ContractWithCustomerLiabilityCurrentCustomerDeposits" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Contract With Customer, Liability, Current, Customer Deposits</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_ContractWithCustomerLiabilityCurrentCustomerDeposits" xlink:href="kai-20260103.xsd#kai_ContractWithCustomerLiabilityCurrentCustomerDeposits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_ContractWithCustomerLiabilityCurrentCustomerDeposits" xlink:to="lab_kai_ContractWithCustomerLiabilityCurrentCustomerDeposits" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityRegistrantName_691662d2-3177-467a-80ef-4adb5294b704_terseLabel_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:label id="lab_dei_EntityRegistrantName_label_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityRegistrantName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityRegistrantName" xlink:to="lab_dei_EntityRegistrantName" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method</link:label>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_label_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_StkPrcOrTsrEstimationMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:to="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_SupplementalBalanceSheetInformationRelatedtoLeasesTableTextBlock_b7f33cc9-d072-4a71-80c6-90ef5d3d8932_terseLabel_en-US" xlink:label="lab_kai_SupplementalBalanceSheetInformationRelatedtoLeasesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Supplemental balance sheet information</link:label>
    <link:label id="lab_kai_SupplementalBalanceSheetInformationRelatedtoLeasesTableTextBlock_label_en-US" xlink:label="lab_kai_SupplementalBalanceSheetInformationRelatedtoLeasesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Supplemental Balance Sheet Information Related to Leases [Table Text Block]</link:label>
    <link:label id="lab_kai_SupplementalBalanceSheetInformationRelatedtoLeasesTableTextBlock_documentation_en-US" xlink:label="lab_kai_SupplementalBalanceSheetInformationRelatedtoLeasesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Supplemental Balance Sheet Information Related to Leases [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_SupplementalBalanceSheetInformationRelatedtoLeasesTableTextBlock" xlink:href="kai-20260103.xsd#kai_SupplementalBalanceSheetInformationRelatedtoLeasesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_SupplementalBalanceSheetInformationRelatedtoLeasesTableTextBlock" xlink:to="lab_kai_SupplementalBalanceSheetInformationRelatedtoLeasesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_IndustrialProcessingMember_22ab086f-e04f-4f3e-9645-1e7f52ba2d0d_terseLabel_en-US" xlink:label="lab_kai_IndustrialProcessingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Industrial Processing</link:label>
    <link:label id="lab_kai_IndustrialProcessingMember_label_en-US" xlink:label="lab_kai_IndustrialProcessingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Industrial Processing [Member]</link:label>
    <link:label id="lab_kai_IndustrialProcessingMember_documentation_en-US" xlink:label="lab_kai_IndustrialProcessingMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Industrial Processing</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_IndustrialProcessingMember" xlink:href="kai-20260103.xsd#kai_IndustrialProcessingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_IndustrialProcessingMember" xlink:to="lab_kai_IndustrialProcessingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseRightOfUseAssetBeforeAccumulatedAmortization_19c50117-e9a6-4125-94d0-cfbfe3ca4b7a_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseRightOfUseAssetBeforeAccumulatedAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">ROU assets, at cost</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseRightOfUseAssetBeforeAccumulatedAmortization_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseRightOfUseAssetBeforeAccumulatedAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Right-of-Use Asset, before Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseRightOfUseAssetBeforeAccumulatedAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseRightOfUseAssetBeforeAccumulatedAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseRightOfUseAssetBeforeAccumulatedAmortization" xlink:to="lab_us-gaap_FinanceLeaseRightOfUseAssetBeforeAccumulatedAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_JointVentureWithItalianCompanyMember_139d5cdc-b1c0-403d-9138-a7cad47042b3_terseLabel_en-US" xlink:label="lab_kai_JointVentureWithItalianCompanyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Joint Venture with an Italian Company</link:label>
    <link:label id="lab_kai_JointVentureWithItalianCompanyMember_label_en-US" xlink:label="lab_kai_JointVentureWithItalianCompanyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Joint Venture With Italian Company [Member]</link:label>
    <link:label id="lab_kai_JointVentureWithItalianCompanyMember_documentation_en-US" xlink:label="lab_kai_JointVentureWithItalianCompanyMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Joint Venture With Italian Company [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_JointVentureWithItalianCompanyMember" xlink:href="kai-20260103.xsd#kai_JointVentureWithItalianCompanyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_JointVentureWithItalianCompanyMember" xlink:to="lab_kai_JointVentureWithItalianCompanyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_BusinessAcquisitionIntangibleAssetsOtherThanGoodwillExpectedTaxDeductibleAmount_b908a4ef-50fd-4831-8e5a-d6000e140215_terseLabel_en-US" xlink:label="lab_kai_BusinessAcquisitionIntangibleAssetsOtherThanGoodwillExpectedTaxDeductibleAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible assets other than goodwill, expected tax deductible amount</link:label>
    <link:label id="lab_kai_BusinessAcquisitionIntangibleAssetsOtherThanGoodwillExpectedTaxDeductibleAmount_label_en-US" xlink:label="lab_kai_BusinessAcquisitionIntangibleAssetsOtherThanGoodwillExpectedTaxDeductibleAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Acquisition, Intangible Assets, Other Than Goodwill, Expected Tax Deductible Amount</link:label>
    <link:label id="lab_kai_BusinessAcquisitionIntangibleAssetsOtherThanGoodwillExpectedTaxDeductibleAmount_documentation_en-US" xlink:label="lab_kai_BusinessAcquisitionIntangibleAssetsOtherThanGoodwillExpectedTaxDeductibleAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Acquisition, Intangible Assets, Other Than Goodwill, Expected Tax Deductible Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_BusinessAcquisitionIntangibleAssetsOtherThanGoodwillExpectedTaxDeductibleAmount" xlink:href="kai-20260103.xsd#kai_BusinessAcquisitionIntangibleAssetsOtherThanGoodwillExpectedTaxDeductibleAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_BusinessAcquisitionIntangibleAssetsOtherThanGoodwillExpectedTaxDeductibleAmount" xlink:to="lab_kai_BusinessAcquisitionIntangibleAssetsOtherThanGoodwillExpectedTaxDeductibleAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDebtTableTextBlock_baed52a0-4875-4192-944d-5fff59bac413_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term obligations</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDebtTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Debt [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDebtTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfDebtTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDebtTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MachineryAndEquipmentMember_f3f1008b-85a2-444e-ade0-d51bfef75883_terseLabel_en-US" xlink:label="lab_us-gaap_MachineryAndEquipmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Machinery and Equipment</link:label>
    <link:label id="lab_us-gaap_MachineryAndEquipmentMember_label_en-US" xlink:label="lab_us-gaap_MachineryAndEquipmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Machinery and Equipment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MachineryAndEquipmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MachineryAndEquipmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MachineryAndEquipmentMember" xlink:to="lab_us-gaap_MachineryAndEquipmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_814e2746-2422-4219-b24c-7370041f2b85_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average grant date fair value, granted (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period, Weighted Average Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDateAxis_terseLabel_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date:</link:label>
    <link:label id="lab_ecd_RestatementDateAxis_label_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDateAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_RestatementDateAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDateAxis" xlink:to="lab_ecd_RestatementDateAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation_f12923ba-348c-4894-b114-009cfc7d7feb_verboseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Activity under stock plans</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Shares Issued, Value, Share-Based Payment Arrangement, after Forfeiture</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredForeignIncomeTaxExpenseBenefit_9a63a24e-1f24-44d8-a284-2b7129244390_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredForeignIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign</link:label>
    <link:label id="lab_us-gaap_DeferredForeignIncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_DeferredForeignIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Foreign Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredForeignIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredForeignIncomeTaxExpenseBenefit"/>
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    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable_b03a6a85-f2a5-4647-a9e8-b91598994353_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income Loss [Table]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRestructuringAndRelatedCostsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfRestructuringAndRelatedCostsTextBlock"/>
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    <link:label id="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities_label_en-US" xlink:label="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from (Payment for) Other Financing Activity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromPaymentsForOtherFinancingActivities"/>
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    <link:label id="lab_us-gaap_BusinessAcquisitionProFormaEarningsPerShareDiluted_bafd9ed5-3925-46d3-9844-2dc07a94f469_verboseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionProFormaEarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Diluted (in dollars per share)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract"/>
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    <link:label id="lab_kai_ClydeIndustriesMember_019b8225-08af-76e8-976a-ef4489ac6960_terseLabel_en-US" xlink:label="lab_kai_ClydeIndustriesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Clyde Industries</link:label>
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    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
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    <link:label id="lab_us-gaap_PaymentsForRestructuring_7b791d4f-d82d-4733-925a-0ab64612b151_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsForRestructuring" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Usage</link:label>
    <link:label id="lab_us-gaap_PaymentsForRestructuring_label_en-US" xlink:label="lab_us-gaap_PaymentsForRestructuring" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments for Restructuring</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_IcfrAuditorAttestationFlag" xlink:to="lab_dei_IcfrAuditorAttestationFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_CashFlowNoncashFinancingActivitiesDisclosureAbstract_08aa708a-3e60-4ce7-8747-668c662b2b14_terseLabel_en-US" xlink:label="lab_kai_CashFlowNoncashFinancingActivitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Cash Financing Activities:</link:label>
    <link:label id="lab_kai_CashFlowNoncashFinancingActivitiesDisclosureAbstract_label_en-US" xlink:label="lab_kai_CashFlowNoncashFinancingActivitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Flow, Noncash Financing Activities Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_CashFlowNoncashFinancingActivitiesDisclosureAbstract" xlink:href="kai-20260103.xsd#kai_CashFlowNoncashFinancingActivitiesDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_CashFlowNoncashFinancingActivitiesDisclosureAbstract" xlink:to="lab_kai_CashFlowNoncashFinancingActivitiesDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityMaturityTableTextBlock_85a3bc19-b50d-46cd-b962-48863ec3a6db_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Future lease payments for finance lease liabilities</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityMaturityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid, Maturity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityMaturityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiabilityMaturityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilityMaturityTableTextBlock" xlink:to="lab_us-gaap_FinanceLeaseLiabilityMaturityTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByLiabilityClassAxis_8eb577ba-4d1f-4e01-86b0-892d7eb0e2f9_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByLiabilityClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liability Class [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByLiabilityClassAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByLiabilityClassAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability Class [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByLiabilityClassAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByLiabilityClassAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByLiabilityClassAxis" xlink:to="lab_us-gaap_FairValueByLiabilityClassAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StandardProductWarrantyAccrualForeignCurrencyTranslationGainLoss_4d7e2278-3d00-40b7-9716-6e56d406b3ab_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_StandardProductWarrantyAccrualForeignCurrencyTranslationGainLoss" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Currency translation</link:label>
    <link:label id="lab_us-gaap_StandardProductWarrantyAccrualForeignCurrencyTranslationGainLoss_label_en-US" xlink:label="lab_us-gaap_StandardProductWarrantyAccrualForeignCurrencyTranslationGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Standard Product Warranty Accrual, Foreign Currency Translation Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StandardProductWarrantyAccrualForeignCurrencyTranslationGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StandardProductWarrantyAccrualForeignCurrencyTranslationGainLoss"/>
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    <link:label id="lab_us-gaap_ForeignCountryMember_dad3c806-e731-4ec8-ad3b-5a5f9d209751_terseLabel_en-US" xlink:label="lab_us-gaap_ForeignCountryMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign tax authority</link:label>
    <link:label id="lab_us-gaap_ForeignCountryMember_label_en-US" xlink:label="lab_us-gaap_ForeignCountryMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Foreign Tax Jurisdiction [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignCountryMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ForeignCountryMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ForeignCountryMember" xlink:to="lab_us-gaap_ForeignCountryMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AuditorFirmId_510d5cac-e272-4d53-8568-72c0515f1e9f_terseLabel_en-US" xlink:label="lab_dei_AuditorFirmId" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Auditor Firm ID</link:label>
    <link:label id="lab_dei_AuditorFirmId_label_en-US" xlink:label="lab_dei_AuditorFirmId" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Auditor Firm ID</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AuditorFirmId" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_AuditorFirmId"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_AuditorFirmId" xlink:to="lab_dei_AuditorFirmId" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentDomain_55fcd26c-7429-4d5a-b02d-7ed300feb67b_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segments [Domain]</link:label>
    <link:label id="lab_us-gaap_SegmentDomain_label_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentDomain" xlink:to="lab_us-gaap_SegmentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_BusinessAcquisitionGoodwillExpectedTaxDeductibleTerm_433c0290-e9ef-46c4-acee-68a863e40490_terseLabel_en-US" xlink:label="lab_kai_BusinessAcquisitionGoodwillExpectedTaxDeductibleTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill, expected deductible term (in years)</link:label>
    <link:label id="lab_kai_BusinessAcquisitionGoodwillExpectedTaxDeductibleTerm_label_en-US" xlink:label="lab_kai_BusinessAcquisitionGoodwillExpectedTaxDeductibleTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Acquisition, Goodwill, Expected Tax Deductible Term</link:label>
    <link:label id="lab_kai_BusinessAcquisitionGoodwillExpectedTaxDeductibleTerm_documentation_en-US" xlink:label="lab_kai_BusinessAcquisitionGoodwillExpectedTaxDeductibleTerm" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Acquisition, Goodwill, Expected Tax Deductible Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_BusinessAcquisitionGoodwillExpectedTaxDeductibleTerm" xlink:href="kai-20260103.xsd#kai_BusinessAcquisitionGoodwillExpectedTaxDeductibleTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_BusinessAcquisitionGoodwillExpectedTaxDeductibleTerm" xlink:to="lab_kai_BusinessAcquisitionGoodwillExpectedTaxDeductibleTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementLocationAxis_d76dd7cf-394a-4247-9f79-b0a16889a915_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Income Location, Balance [Axis]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementLocationAxis_label_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Income Location, Balance [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementLocationAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementLocationAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementLocationAxis" xlink:to="lab_us-gaap_IncomeStatementLocationAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesForeign_52cb83aa-9bd3-44c6-98a5-c415291d1955_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesForeign" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesForeign_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesForeign" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Continuing Operations before Income Taxes, Foreign</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesForeign" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesForeign"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesForeign" xlink:to="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesForeign" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity_1d0b57bc-034f-49da-b1ff-f5716005b2c6_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Remaining borrowing capacity</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Remaining Borrowing Capacity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:to="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_ff7d8b94-a605-4bf8-96c0-f17e02271f9f_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInInventories_0ecd32bd-837d-4138-8bc7-214882ef51a9_negatedLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInInventories" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Inventories</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInInventories_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInInventories" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Inventories</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInInventories" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInInventories"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInInventories" xlink:to="lab_us-gaap_IncreaseDecreaseInInventories" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_BusinessCombinationAcquisitionOfSubsidiarySharesFromNoncontrollingInterest_462140ea-bcd9-4615-888e-9fa8f144f1b7_negatedTerseLabel_en-US" xlink:label="lab_kai_BusinessCombinationAcquisitionOfSubsidiarySharesFromNoncontrollingInterest" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Acquisition of subsidiary shares from noncontrolling interest (Note 2)</link:label>
    <link:label id="lab_kai_BusinessCombinationAcquisitionOfSubsidiarySharesFromNoncontrollingInterest_4000464f-c81e-4329-b73a-3ca7b8114881_terseLabel_en-US" xlink:label="lab_kai_BusinessCombinationAcquisitionOfSubsidiarySharesFromNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquisition of subsidiary shares from noncontrolling interest</link:label>
    <link:label id="lab_kai_BusinessCombinationAcquisitionOfSubsidiarySharesFromNoncontrollingInterest_label_en-US" xlink:label="lab_kai_BusinessCombinationAcquisitionOfSubsidiarySharesFromNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Acquisition Of Subsidiary Shares From Noncontrolling Interest</link:label>
    <link:label id="lab_kai_BusinessCombinationAcquisitionOfSubsidiarySharesFromNoncontrollingInterest_documentation_en-US" xlink:label="lab_kai_BusinessCombinationAcquisitionOfSubsidiarySharesFromNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Acquisition Of Subsidiary Shares From Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_BusinessCombinationAcquisitionOfSubsidiarySharesFromNoncontrollingInterest" xlink:href="kai-20260103.xsd#kai_BusinessCombinationAcquisitionOfSubsidiarySharesFromNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_BusinessCombinationAcquisitionOfSubsidiarySharesFromNoncontrollingInterest" xlink:to="lab_kai_BusinessCombinationAcquisitionOfSubsidiarySharesFromNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_SaleOfPropertyPlantAndEquipmentDownPaymentPercentReceived_3de639a8-33bc-4777-a297-27d41a5b5089_terseLabel_en-US" xlink:label="lab_kai_SaleOfPropertyPlantAndEquipmentDownPaymentPercentReceived" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Down payment (percentage)</link:label>
    <link:label id="lab_kai_SaleOfPropertyPlantAndEquipmentDownPaymentPercentReceived_label_en-US" xlink:label="lab_kai_SaleOfPropertyPlantAndEquipmentDownPaymentPercentReceived" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale Of Property, Plant, And Equipment, Down Payment, Percent Received</link:label>
    <link:label id="lab_kai_SaleOfPropertyPlantAndEquipmentDownPaymentPercentReceived_documentation_en-US" xlink:label="lab_kai_SaleOfPropertyPlantAndEquipmentDownPaymentPercentReceived" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Sale Of Property, Plant, And Equipment, Down Payment, Percent Received</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_SaleOfPropertyPlantAndEquipmentDownPaymentPercentReceived" xlink:href="kai-20260103.xsd#kai_SaleOfPropertyPlantAndEquipmentDownPaymentPercentReceived"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_SaleOfPropertyPlantAndEquipmentDownPaymentPercentReceived" xlink:to="lab_kai_SaleOfPropertyPlantAndEquipmentDownPaymentPercentReceived" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsOther_019bb2ab-b494-7f19-8754-50cd3248ce0f_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsOther" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Other, tax credits</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsOther_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsOther" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Tax Credit, Other, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsOther" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsOther"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsOther" xlink:to="lab_us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsOther" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerSharePolicyTextBlock_5d54d66f-3577-4d1c-8e75-83a3a81b1b7a_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerSharePolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings per Share</link:label>
    <link:label id="lab_us-gaap_EarningsPerSharePolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_EarningsPerSharePolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerSharePolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerSharePolicyTextBlock"/>
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    <link:label id="lab_us-gaap_AcquisitionRelatedCostsMember_24a816a0-7267-4678-b8d3-0ee67bad6289_terseLabel_en-US" xlink:label="lab_us-gaap_AcquisitionRelatedCostsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Pro Forma Information, Nonrecurring Adjustment, Acquisition-Related Cost</link:label>
    <link:label id="lab_us-gaap_AcquisitionRelatedCostsMember_label_en-US" xlink:label="lab_us-gaap_AcquisitionRelatedCostsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Pro Forma Information, Nonrecurring Adjustment, Acquisition-Related Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AcquisitionRelatedCostsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AcquisitionRelatedCostsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AcquisitionRelatedCostsMember" xlink:to="lab_us-gaap_AcquisitionRelatedCostsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtAndCapitalLeaseObligationsIncludingCurrentMaturities_82e16e43-6aaa-4ff4-b94e-e001f09c0ac1_totalLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtAndCapitalLeaseObligationsIncludingCurrentMaturities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_LongTermDebtAndCapitalLeaseObligationsIncludingCurrentMaturities_label_en-US" xlink:label="lab_us-gaap_LongTermDebtAndCapitalLeaseObligationsIncludingCurrentMaturities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt and Lease Obligation, Including Current Maturities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtAndCapitalLeaseObligationsIncludingCurrentMaturities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebtAndCapitalLeaseObligationsIncludingCurrentMaturities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtAndCapitalLeaseObligationsIncludingCurrentMaturities" xlink:to="lab_us-gaap_LongTermDebtAndCapitalLeaseObligationsIncludingCurrentMaturities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueRecognitionPolicyTextBlock_8f153c94-791b-4c45-8ad6-543658a5e4fe_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueRecognitionPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue Recognition</link:label>
    <link:label id="lab_us-gaap_RevenueRecognitionPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_RevenueRecognitionPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueRecognitionPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenueRecognitionPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueRecognitionPolicyTextBlock" xlink:to="lab_us-gaap_RevenueRecognitionPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SeniorNotesMember_0c067425-1c6c-4742-af58-03ee435db2c9_terseLabel_en-US" xlink:label="lab_us-gaap_SeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Senior Promissory Notes, due 2026 to 2028</link:label>
    <link:label id="lab_us-gaap_SeniorNotesMember_b10765ec-678f-4089-8cc5-c134fc1e4003_verboseLabel_en-US" xlink:label="lab_us-gaap_SeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Senior promissory notes</link:label>
    <link:label id="lab_us-gaap_SeniorNotesMember_label_en-US" xlink:label="lab_us-gaap_SeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Senior Notes [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeniorNotesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SeniorNotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeniorNotesMember" xlink:to="lab_us-gaap_SeniorNotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockValue_7b1714ee-94d3-441b-8e6b-248522f3b6b3_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, $.01 par value, 5,000,000 shares authorized; none issued</link:label>
    <link:label id="lab_us-gaap_PreferredStockValue_label_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockValue" xlink:to="lab_us-gaap_PreferredStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities_6e40f5ad-b9df-4dcf-84dd-d640b348d33d_totalLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities assumed</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities"/>
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    <link:label id="lab_kai_WoodProcessingSystemsSegmentMember_57b3440b-a166-4b88-bac5-7d2d21d65aff_terseLabel_en-US" xlink:label="lab_kai_WoodProcessingSystemsSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Wood Processing</link:label>
    <link:label id="lab_kai_WoodProcessingSystemsSegmentMember_label_en-US" xlink:label="lab_kai_WoodProcessingSystemsSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Wood Processing Systems Segment [Member]</link:label>
    <link:label id="lab_kai_WoodProcessingSystemsSegmentMember_documentation_en-US" xlink:label="lab_kai_WoodProcessingSystemsSegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Operating segment product line</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_WoodProcessingSystemsSegmentMember" xlink:href="kai-20260103.xsd#kai_WoodProcessingSystemsSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_WoodProcessingSystemsSegmentMember" xlink:to="lab_kai_WoodProcessingSystemsSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_terseLabel_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Executive Categories</link:label>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_label_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Executive Categories [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllExecutiveCategoriesMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AllExecutiveCategoriesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllExecutiveCategoriesMember" xlink:to="lab_ecd_AllExecutiveCategoriesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock_3382a005-3ec4-4c29-85d0-1bbd1748a03b_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net deferred tax (liability) asset</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Deferred Tax Assets and Liabilities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_FiberProcessingMember_ee37098a-9f3c-43cd-9419-e0b31a66d2e3_terseLabel_en-US" xlink:label="lab_kai_FiberProcessingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fiber Processing</link:label>
    <link:label id="lab_kai_FiberProcessingMember_label_en-US" xlink:label="lab_kai_FiberProcessingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fiber Processing [Member]</link:label>
    <link:label id="lab_kai_FiberProcessingMember_documentation_en-US" xlink:label="lab_kai_FiberProcessingMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fiber Processing</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_FiberProcessingMember" xlink:href="kai-20260103.xsd#kai_FiberProcessingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_FiberProcessingMember" xlink:to="lab_kai_FiberProcessingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryFinishedGoodsNetOfReserves_6df6bc8a-06fa-445d-9275-ddfaceabfb10_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryFinishedGoodsNetOfReserves" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finished Goods (includes $3,556 and $554 at customer locations)</link:label>
    <link:label id="lab_us-gaap_InventoryFinishedGoodsNetOfReserves_label_en-US" xlink:label="lab_us-gaap_InventoryFinishedGoodsNetOfReserves" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Inventory, Finished Goods, Net of Reserves</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryFinishedGoodsNetOfReserves" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InventoryFinishedGoodsNetOfReserves"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryFinishedGoodsNetOfReserves" xlink:to="lab_us-gaap_InventoryFinishedGoodsNetOfReserves" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockValue_19bbf4c4-ed7e-432d-a930-841277f7183c_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, $.01 par value, 150,000,000 shares authorized; 14,624,159 shares issued</link:label>
    <link:label id="lab_us-gaap_CommonStockValue_label_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockValue" xlink:to="lab_us-gaap_CommonStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseRightOfUseAsset_3b798360-e94c-48c2-b19b-cffe5fd80285_totalLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">ROU assets, net</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseRightOfUseAsset_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Right-of-Use Asset, after Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseRightOfUseAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseRightOfUseAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseRightOfUseAsset" xlink:to="lab_us-gaap_FinanceLeaseRightOfUseAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_IndefiniteLivedIntangibleAssetsExcludingGoodwillGross_945e85ba-2271-4db4-80d0-da061c360f93_terseLabel_en-US" xlink:label="lab_kai_IndefiniteLivedIntangibleAssetsExcludingGoodwillGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross</link:label>
    <link:label id="lab_kai_IndefiniteLivedIntangibleAssetsExcludingGoodwillGross_label_en-US" xlink:label="lab_kai_IndefiniteLivedIntangibleAssetsExcludingGoodwillGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Indefinite-Lived Intangible Assets (Excluding Goodwill), Gross</link:label>
    <link:label id="lab_kai_IndefiniteLivedIntangibleAssetsExcludingGoodwillGross_documentation_en-US" xlink:label="lab_kai_IndefiniteLivedIntangibleAssetsExcludingGoodwillGross" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Indefinite-Lived Intangible Assets (Excluding Goodwill), Gross</link:label>
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    <link:label id="lab_srt_TitleOfIndividualAxis_abc4bb12-db2e-4aea-9d2d-2f5f76249327_terseLabel_en-US" xlink:label="lab_srt_TitleOfIndividualAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title and Position [Axis]</link:label>
    <link:label id="lab_srt_TitleOfIndividualAxis_label_en-US" xlink:label="lab_srt_TitleOfIndividualAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Title and Position [Axis]</link:label>
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    <link:label id="lab_us-gaap_CommitmentsAndContingencies_09f640c3-6f27-470c-82cb-a0c1e664f040_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies (Note 7)</link:label>
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    <link:label id="lab_us-gaap_InventoryRawMaterialsAndSuppliesNetOfReserves_ea78e713-1fc4-4420-a9ef-d5e0a6f40838_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryRawMaterialsAndSuppliesNetOfReserves" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Raw Materials</link:label>
    <link:label id="lab_us-gaap_InventoryRawMaterialsAndSuppliesNetOfReserves_label_en-US" xlink:label="lab_us-gaap_InventoryRawMaterialsAndSuppliesNetOfReserves" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Inventory, Raw Materials and Supplies, Net of Reserves</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryRawMaterialsAndSuppliesNetOfReserves" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InventoryRawMaterialsAndSuppliesNetOfReserves"/>
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    <link:label id="lab_us-gaap_BusinessAcquisitionAxis_3f8eb765-a1ea-4ae4-99f2-99403eda827f_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination [Axis]</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionAxis_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Axis]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest"/>
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    <link:label id="lab_us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleTable_81b2cbbd-c5aa-4512-b347-a38a35e804eb_terseLabel_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nature of Operations [Table]</link:label>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleTable_label_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounting Standards Update and Change in Accounting Principle [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleTable"/>
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    <link:label id="lab_kai_BankersAcceptanceDraftsPolicyPolicyTextBlock_869b601b-1b15-4206-a1b1-9516f9f0f444_terseLabel_en-US" xlink:label="lab_kai_BankersAcceptanceDraftsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Banker's Acceptance Drafts Included in Accounts Receivable</link:label>
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    <link:label id="lab_us-gaap_NoncontrollingInterestMember_ffb5b0c3-768b-4da5-bb28-56f7db8a0de8_terseLabel_en-US" xlink:label="lab_us-gaap_NoncontrollingInterestMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncontrolling Interests</link:label>
    <link:label id="lab_us-gaap_NoncontrollingInterestMember_label_en-US" xlink:label="lab_us-gaap_NoncontrollingInterestMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncontrollingInterestMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NoncontrollingInterestMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoncontrollingInterestMember" xlink:to="lab_us-gaap_NoncontrollingInterestMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityInterestAccretion_019bb2d0-bd56-7b4d-b7dd-6fca175a7ac2_negatedTerseLabel_en-US" xlink:label="lab_kai_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityInterestAccretion" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Interest accretion</link:label>
    <link:label id="lab_kai_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityInterestAccretion_label_en-US" xlink:label="lab_kai_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityInterestAccretion" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement With Unobservable Inputs Reconciliation, Recurring Basis, Liability, Interest Accretion</link:label>
    <link:label id="lab_kai_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityInterestAccretion_documentation_en-US" xlink:label="lab_kai_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityInterestAccretion" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement With Unobservable Inputs Reconciliation, Recurring Basis, Liability, Interest Accretion</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityInterestAccretion" xlink:href="kai-20260103.xsd#kai_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityInterestAccretion"/>
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    <link:label id="lab_us-gaap_OtherNonoperatingExpense_3cf9f71a-2970-4b11-8eb4-7f768023e9f7_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_OtherNonoperatingExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Other Expense, Net</link:label>
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    <link:label id="lab_ecd_PeoActuallyPaidCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoActuallyPaidCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Actually Paid Compensation Amount</link:label>
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    <link:label id="lab_us-gaap_DebtInstrumentFairValue_cc5928c6-096a-4ce5-8c9d-ec860d81a6e9_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt obligations</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentFairValue_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentFairValue"/>
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    <link:label id="lab_us-gaap_DerivativeContractTypeDomain_f7904a0c-7eb0-4390-ad8f-f84599aee3c2_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeContractTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Contract [Domain]</link:label>
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    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfCommonStock_c5b21cd4-d230-4272-bef6-530d97b8dabd_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from issuance of Company common stock</link:label>
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    <link:label id="lab_ecd_AllIndividualsMember_terseLabel_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Individuals</link:label>
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    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_4ef756ed-22b7-4edc-99cf-fcb00aab7d28_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term Debt, Type [Domain]</link:label>
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    <link:label id="lab_us-gaap_ContractTerminationMember_1b32768a-747d-4892-beb8-019c53105093_terseLabel_en-US" xlink:label="lab_us-gaap_ContractTerminationMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contract Termination Costs</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractTerminationMember" xlink:to="lab_us-gaap_ContractTerminationMember" xlink:type="arc" order="1"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosuresAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresAbstract" xlink:to="lab_us-gaap_FairValueDisclosuresAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_ce62f3e9-f798-43a7-896f-8ff6de1e85b8_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Purchases of property, plant, and equipment</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Property, Plant, and Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquirePropertyPlantAndEquipment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:to="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TransferredAtPointInTimeMember_807fb7a2-6eb0-4cd2-b78b-1f665f036ed6_terseLabel_en-US" xlink:label="lab_us-gaap_TransferredAtPointInTimeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Point in Time</link:label>
    <link:label id="lab_us-gaap_TransferredAtPointInTimeMember_label_en-US" xlink:label="lab_us-gaap_TransferredAtPointInTimeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Transferred at Point in Time [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransferredAtPointInTimeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransferredAtPointInTimeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TransferredAtPointInTimeMember" xlink:to="lab_us-gaap_TransferredAtPointInTimeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryIndName" xlink:to="lab_ecd_ForgoneRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_label_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:to="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeMember_5485da41-9c59-476c-a289-1debc0d68b1d_terseLabel_en-US" xlink:label="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reclassification out of Accumulated Other Comprehensive Income</link:label>
    <link:label id="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeMember_label_en-US" xlink:label="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reclassification out of Accumulated Other Comprehensive Income [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeMember" xlink:to="lab_us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillForeignCurrencyTranslationGainLoss_7ebdbd73-5437-46ec-8447-cdad7664cd1b_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillForeignCurrencyTranslationGainLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Currency translation</link:label>
    <link:label id="lab_us-gaap_GoodwillForeignCurrencyTranslationGainLoss_label_en-US" xlink:label="lab_us-gaap_GoodwillForeignCurrencyTranslationGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill, Foreign Currency Translation, Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillForeignCurrencyTranslationGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillForeignCurrencyTranslationGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillForeignCurrencyTranslationGainLoss" xlink:to="lab_us-gaap_GoodwillForeignCurrencyTranslationGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_KWSManufacturingCompanyLimitedKWSMember_ce20273c-0d5c-4435-9ba7-b992e5117762_terseLabel_en-US" xlink:label="lab_kai_KWSManufacturingCompanyLimitedKWSMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">KWS</link:label>
    <link:label id="lab_kai_KWSManufacturingCompanyLimitedKWSMember_label_en-US" xlink:label="lab_kai_KWSManufacturingCompanyLimitedKWSMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">KWS Manufacturing Company Limited ("KWS") [Member]</link:label>
    <link:label id="lab_kai_KWSManufacturingCompanyLimitedKWSMember_documentation_en-US" xlink:label="lab_kai_KWSManufacturingCompanyLimitedKWSMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">KWS Manufacturing Company Limited ("KWS")</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_KWSManufacturingCompanyLimitedKWSMember" xlink:href="kai-20260103.xsd#kai_KWSManufacturingCompanyLimitedKWSMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_KWSManufacturingCompanyLimitedKWSMember" xlink:to="lab_kai_KWSManufacturingCompanyLimitedKWSMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis</link:label>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_label_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompAnalysisTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ErrCompAnalysisTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompAnalysisTextBlock" xlink:to="lab_ecd_ErrCompAnalysisTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityLineItems_55eecc21-6ba9-477a-bb46-acce329e3f8a_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of Credit Facility [Line Items]</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityLineItems_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LineOfCreditFacilityLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityLineItems" xlink:to="lab_us-gaap_LineOfCreditFacilityLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherBorrowings_02018a0c-8711-45af-a693-7f8d3ab25882_terseLabel_en-US" xlink:label="lab_us-gaap_OtherBorrowings" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Borrowings, due 2026 to 2031</link:label>
    <link:label id="lab_us-gaap_OtherBorrowings_label_en-US" xlink:label="lab_us-gaap_OtherBorrowings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Borrowings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherBorrowings" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherBorrowings"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherBorrowings" xlink:to="lab_us-gaap_OtherBorrowings" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_StatementGeographicalAxis_f12d96d0-d04e-4274-a74c-f6ab5fd27936_terseLabel_en-US" xlink:label="lab_srt_StatementGeographicalAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Geographical [Axis]</link:label>
    <link:label id="lab_srt_StatementGeographicalAxis_label_en-US" xlink:label="lab_srt_StatementGeographicalAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Geographical [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StatementGeographicalAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StatementGeographicalAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_StatementGeographicalAxis" xlink:to="lab_srt_StatementGeographicalAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_GoodwillByReportingUnitTableTextBlock_b2255bbe-0857-45de-8a7b-42e94a38d772_terseLabel_en-US" xlink:label="lab_kai_GoodwillByReportingUnitTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill by reporting unit</link:label>
    <link:label id="lab_kai_GoodwillByReportingUnitTableTextBlock_label_en-US" xlink:label="lab_kai_GoodwillByReportingUnitTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill by Reporting Unit [Table Text Block]</link:label>
    <link:label id="lab_kai_GoodwillByReportingUnitTableTextBlock_documentation_en-US" xlink:label="lab_kai_GoodwillByReportingUnitTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Tabular disclosure of goodwill and intangible assets, which may be broken down by segment or major class.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_GoodwillByReportingUnitTableTextBlock" xlink:href="kai-20260103.xsd#kai_GoodwillByReportingUnitTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_GoodwillByReportingUnitTableTextBlock" xlink:to="lab_kai_GoodwillByReportingUnitTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeLeaseDescriptionLineItems_062d02d9-dc81-441f-a5ea-3f65aacda677_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeLeaseDescriptionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lessee, Lease, Description [Line Items]</link:label>
    <link:label id="lab_us-gaap_LesseeLeaseDescriptionLineItems_label_en-US" xlink:label="lab_us-gaap_LesseeLeaseDescriptionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Lease, Description [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeLeaseDescriptionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeLeaseDescriptionLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeLeaseDescriptionLineItems" xlink:to="lab_us-gaap_LesseeLeaseDescriptionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_Rule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:to="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionsProFormaRevenue_6b1f161a-eb00-4587-83d9-d57ca78dee5c_verboseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionsProFormaRevenue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Revenue</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionsProFormaRevenue_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionsProFormaRevenue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Pro Forma Information, Pro Forma Revenue</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionsProFormaRevenue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionsProFormaRevenue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionsProFormaRevenue" xlink:to="lab_us-gaap_BusinessAcquisitionsProFormaRevenue" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_PropertyPlantandEquipmentandFinanceLeaseRightofUseAssetDepreciationandAmortizationExpense_0d952e09-84e7-4783-8f93-2e2923dfcfb1_terseLabel_en-US" xlink:label="lab_kai_PropertyPlantandEquipmentandFinanceLeaseRightofUseAssetDepreciationandAmortizationExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation and amortization expense for property, plant and equipment and finance lease right-of-use asset</link:label>
    <link:label id="lab_kai_PropertyPlantandEquipmentandFinanceLeaseRightofUseAssetDepreciationandAmortizationExpense_label_en-US" xlink:label="lab_kai_PropertyPlantandEquipmentandFinanceLeaseRightofUseAssetDepreciationandAmortizationExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment and Finance Lease Right-of-Use Asset, Depreciation and Amortization Expense</link:label>
    <link:label id="lab_kai_PropertyPlantandEquipmentandFinanceLeaseRightofUseAssetDepreciationandAmortizationExpense_documentation_en-US" xlink:label="lab_kai_PropertyPlantandEquipmentandFinanceLeaseRightofUseAssetDepreciationandAmortizationExpense" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment and Finance Lease Right-of-Use Asset, Depreciation and Amortization Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_PropertyPlantandEquipmentandFinanceLeaseRightofUseAssetDepreciationandAmortizationExpense" xlink:href="kai-20260103.xsd#kai_PropertyPlantandEquipmentandFinanceLeaseRightofUseAssetDepreciationandAmortizationExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_PropertyPlantandEquipmentandFinanceLeaseRightofUseAssetDepreciationandAmortizationExpense" xlink:to="lab_kai_PropertyPlantandEquipmentandFinanceLeaseRightofUseAssetDepreciationandAmortizationExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompRecoveryTable_terseLabel_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery</link:label>
    <link:label id="lab_ecd_ErrCompRecoveryTable_label_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompRecoveryTable" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ErrCompRecoveryTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompRecoveryTable" xlink:to="lab_ecd_ErrCompRecoveryTable" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_Security12bTitle_ac8e5764-e76f-4717-92c1-7290fb38b225_terseLabel_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:label id="lab_dei_Security12bTitle_label_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_Security12bTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_Security12bTitle" xlink:to="lab_dei_Security12bTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeLeaseDescriptionTable_b87a8489-bfd2-463e-90b5-e106177c935d_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeLeaseDescriptionTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lessee, Lease, Description [Table]</link:label>
    <link:label id="lab_us-gaap_LesseeLeaseDescriptionTable_label_en-US" xlink:label="lab_us-gaap_LesseeLeaseDescriptionTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Lease, Description [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeLeaseDescriptionTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeLeaseDescriptionTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeLeaseDescriptionTable" xlink:to="lab_us-gaap_LesseeLeaseDescriptionTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsIncludingIntangibleAssetsPolicyPolicyTextBlock_07070a13-8f16-4e44-a432-0ced5a4eaba8_terseLabel_en-US" xlink:label="lab_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsIncludingIntangibleAssetsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Impairment of Goodwill and Intangible Assets</link:label>
    <link:label id="lab_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsIncludingIntangibleAssetsPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsIncludingIntangibleAssetsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Impairment or Disposal of Long-Lived Assets, Including Intangible Assets, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsIncludingIntangibleAssetsPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ImpairmentOrDisposalOfLongLivedAssetsIncludingIntangibleAssetsPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsIncludingIntangibleAssetsPolicyPolicyTextBlock" xlink:to="lab_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsIncludingIntangibleAssetsPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_ItalianCompanyMember_1f6afcdd-ebb3-45c0-acad-d7de52111294_terseLabel_en-US" xlink:label="lab_kai_ItalianCompanyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Italian Company</link:label>
    <link:label id="lab_kai_ItalianCompanyMember_label_en-US" xlink:label="lab_kai_ItalianCompanyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Italian Company [Member]</link:label>
    <link:label id="lab_kai_ItalianCompanyMember_documentation_en-US" xlink:label="lab_kai_ItalianCompanyMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Italian Company [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_ItalianCompanyMember" xlink:href="kai-20260103.xsd#kai_ItalianCompanyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_ItalianCompanyMember" xlink:to="lab_kai_ItalianCompanyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationTaxCreditsForeign_019c9387-3f53-78dd-ac2f-013a826ad64c_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationTaxCreditsForeign" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Foreign Tax Credit</link:label>
    <link:label id="lab_us-gaap_IncomeTaxReconciliationTaxCreditsForeign_label_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationTaxCreditsForeign" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Tax Credit, Foreign, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReconciliationTaxCreditsForeign" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationTaxCreditsForeign"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxReconciliationTaxCreditsForeign" xlink:to="lab_us-gaap_IncomeTaxReconciliationTaxCreditsForeign" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_fc0908ea-92b6-4588-a5dc-785bae188b38_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareAbstract" xlink:to="lab_us-gaap_EarningsPerShareAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive_03180d71-4cf3-44a8-a867-b230d532bef0_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestructuringPlanAxis_0c441f2f-654e-4a50-9dfe-53a12ff517e8_terseLabel_en-US" xlink:label="lab_us-gaap_RestructuringPlanAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restructuring Plan [Axis]</link:label>
    <link:label id="lab_us-gaap_RestructuringPlanAxis_label_en-US" xlink:label="lab_us-gaap_RestructuringPlanAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restructuring Plan [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestructuringPlanAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestructuringPlanAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestructuringPlanAxis" xlink:to="lab_us-gaap_RestructuringPlanAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByParent_c3be20ad-9361-4cd6-822f-e6cb9b1adeaa_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership interest</link:label>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByParent_label_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsidiary, Ownership Percentage, Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MinorityInterestOwnershipPercentageByParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:to="lab_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesCustomerDeposits_cc8a23e0-581e-44db-97a8-b8c6094bfa55_terseLabel_en-US" xlink:label="lab_kai_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesCustomerDeposits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Customer Deposits</link:label>
    <link:label id="lab_kai_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesCustomerDeposits_label_en-US" xlink:label="lab_kai_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesCustomerDeposits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Current Liabilities, Customer Deposits</link:label>
    <link:label id="lab_kai_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesCustomerDeposits_documentation_en-US" xlink:label="lab_kai_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesCustomerDeposits" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Current Liabilities, Customer Deposits</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesCustomerDeposits" xlink:href="kai-20260103.xsd#kai_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesCustomerDeposits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesCustomerDeposits" xlink:to="lab_kai_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesCustomerDeposits" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_CostOfGoodsAndServicesSoldPreTaxChargeReversal_71c0750e-d695-40a8-98a4-0ac189282c36_terseLabel_en-US" xlink:label="lab_kai_CostOfGoodsAndServicesSoldPreTaxChargeReversal" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase (decrease) in cost of revenue</link:label>
    <link:label id="lab_kai_CostOfGoodsAndServicesSoldPreTaxChargeReversal_label_en-US" xlink:label="lab_kai_CostOfGoodsAndServicesSoldPreTaxChargeReversal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cost of Goods and Services Sold, Pre-Tax Charge (Reversal)</link:label>
    <link:label id="lab_kai_CostOfGoodsAndServicesSoldPreTaxChargeReversal_documentation_en-US" xlink:label="lab_kai_CostOfGoodsAndServicesSoldPreTaxChargeReversal" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Cost of Goods and Services Sold, Pre-Tax Charge (Reversal)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_CostOfGoodsAndServicesSoldPreTaxChargeReversal" xlink:href="kai-20260103.xsd#kai_CostOfGoodsAndServicesSoldPreTaxChargeReversal"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_CostOfGoodsAndServicesSoldPreTaxChargeReversal" xlink:to="lab_kai_CostOfGoodsAndServicesSoldPreTaxChargeReversal" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_SellingGeneralAndAdministrativeExpensePreTaxChargeReversal_717c0f63-0e58-4abf-9483-cf205c073e56_terseLabel_en-US" xlink:label="lab_kai_SellingGeneralAndAdministrativeExpensePreTaxChargeReversal" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase (decrease) in selling, general, and administrative expenses</link:label>
    <link:label id="lab_kai_SellingGeneralAndAdministrativeExpensePreTaxChargeReversal_label_en-US" xlink:label="lab_kai_SellingGeneralAndAdministrativeExpensePreTaxChargeReversal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Selling, General and Administrative Expense, Pre-Tax Charge (Reversal)</link:label>
    <link:label id="lab_kai_SellingGeneralAndAdministrativeExpensePreTaxChargeReversal_documentation_en-US" xlink:label="lab_kai_SellingGeneralAndAdministrativeExpensePreTaxChargeReversal" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Selling, General and Administrative Expense, Pre-Tax Charge (Reversal)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_SellingGeneralAndAdministrativeExpensePreTaxChargeReversal" xlink:href="kai-20260103.xsd#kai_SellingGeneralAndAdministrativeExpensePreTaxChargeReversal"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_SellingGeneralAndAdministrativeExpensePreTaxChargeReversal" xlink:to="lab_kai_SellingGeneralAndAdministrativeExpensePreTaxChargeReversal" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive_07f61935-6790-45da-a24c-7e7b5cf6c717_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2031 and Thereafter</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid, after Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive" xlink:to="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueAfterYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_EmployeeStockPurchasePlanESPPPolicyPolicyTextBlock_fda53ed8-1fec-41fc-b840-243be3cb7ff9_terseLabel_en-US" xlink:label="lab_kai_EmployeeStockPurchasePlanESPPPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Employee Stock Purchase Plan</link:label>
    <link:label id="lab_kai_EmployeeStockPurchasePlanESPPPolicyPolicyTextBlock_label_en-US" xlink:label="lab_kai_EmployeeStockPurchasePlanESPPPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Employee Stock Purchase Plan (ESPP), Policy [Policy Text Block]</link:label>
    <link:label id="lab_kai_EmployeeStockPurchasePlanESPPPolicyPolicyTextBlock_documentation_en-US" xlink:label="lab_kai_EmployeeStockPurchasePlanESPPPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Employee Stock Purchase Plan (ESPP), Policy</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_EmployeeStockPurchasePlanESPPPolicyPolicyTextBlock" xlink:href="kai-20260103.xsd#kai_EmployeeStockPurchasePlanESPPPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_EmployeeStockPurchasePlanESPPPolicyPolicyTextBlock" xlink:to="lab_kai_EmployeeStockPurchasePlanESPPPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgDiscLineItems_label_en-US" xlink:label="lab_ecd_AwardTmgDiscLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Disclosures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgDiscLineItems" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardTmgDiscLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgDiscLineItems" xlink:to="lab_ecd_AwardTmgDiscLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLossCarryforwardsLineItems_16b01188-c134-4efa-96d2-9113a9d0a2bc_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLossCarryforwardsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Loss Carryforwards [Line Items]</link:label>
    <link:label id="lab_us-gaap_OperatingLossCarryforwardsLineItems_label_en-US" xlink:label="lab_us-gaap_OperatingLossCarryforwardsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Loss Carryforwards [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLossCarryforwardsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLossCarryforwardsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLossCarryforwardsLineItems" xlink:to="lab_us-gaap_OperatingLossCarryforwardsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfInventoryCurrentTableTextBlock_4b481151-3306-4c9e-9486-e5cf06c38124_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfInventoryCurrentTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Components of inventory</link:label>
    <link:label id="lab_us-gaap_ScheduleOfInventoryCurrentTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfInventoryCurrentTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Inventory, Current [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInventoryCurrentTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfInventoryCurrentTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfInventoryCurrentTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfInventoryCurrentTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_BankAcceptanceMaturityPeriod_657fd94d-48eb-44c8-acf6-a1c910053d41_terseLabel_en-US" xlink:label="lab_kai_BankAcceptanceMaturityPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maturity period for bank acceptance</link:label>
    <link:label id="lab_kai_BankAcceptanceMaturityPeriod_3c93361e-4dc2-41ee-8d45-a7ba7d0dca01_verboseLabel_en-US" xlink:label="lab_kai_BankAcceptanceMaturityPeriod" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Maturity period for bank acceptance (in months)</link:label>
    <link:label id="lab_kai_BankAcceptanceMaturityPeriod_label_en-US" xlink:label="lab_kai_BankAcceptanceMaturityPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Bank Acceptance, Maturity Period</link:label>
    <link:label id="lab_kai_BankAcceptanceMaturityPeriod_documentation_en-US" xlink:label="lab_kai_BankAcceptanceMaturityPeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Bank Acceptance, Maturity Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_BankAcceptanceMaturityPeriod" xlink:href="kai-20260103.xsd#kai_BankAcceptanceMaturityPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_BankAcceptanceMaturityPeriod" xlink:to="lab_kai_BankAcceptanceMaturityPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestructuringReserveTranslationAdjustment_5d38e4e9-5bcc-4ba2-8a01-6481954bf040_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_RestructuringReserveTranslationAdjustment" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Currency translation</link:label>
    <link:label id="lab_us-gaap_RestructuringReserveTranslationAdjustment_label_en-US" xlink:label="lab_us-gaap_RestructuringReserveTranslationAdjustment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restructuring Reserve, Foreign Currency Translation Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestructuringReserveTranslationAdjustment" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestructuringReserveTranslationAdjustment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestructuringReserveTranslationAdjustment" xlink:to="lab_us-gaap_RestructuringReserveTranslationAdjustment" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_CashFlowNoncashInvestingActivitiesDisclosureAbstract_208d28e3-f25a-4a2b-9e15-027bbfcc01e1_terseLabel_en-US" xlink:label="lab_kai_CashFlowNoncashInvestingActivitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Cash Investing Activities:</link:label>
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    <link:label id="lab_kai_NumberOfSubsidiariesInterestAcquired_212d229a-302e-49e2-bf78-e618f1451b43_terseLabel_en-US" xlink:label="lab_kai_NumberOfSubsidiariesInterestAcquired" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of subsidiaries in which interest was acquired</link:label>
    <link:label id="lab_kai_NumberOfSubsidiariesInterestAcquired_label_en-US" xlink:label="lab_kai_NumberOfSubsidiariesInterestAcquired" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number Of Subsidiaries, Interest Acquired</link:label>
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    <link:label id="lab_us-gaap_CustomerRelationshipsMember_99663116-1595-4e80-80a8-99163724e19a_terseLabel_en-US" xlink:label="lab_us-gaap_CustomerRelationshipsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Customer relationships</link:label>
    <link:label id="lab_us-gaap_CustomerRelationshipsMember_dbda6f3a-f585-4ca4-9dd7-d1f06331d39c_verboseLabel_en-US" xlink:label="lab_us-gaap_CustomerRelationshipsMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Customer relationships</link:label>
    <link:label id="lab_us-gaap_CustomerRelationshipsMember_label_en-US" xlink:label="lab_us-gaap_CustomerRelationshipsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Customer Relationships [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CustomerRelationshipsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CustomerRelationshipsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CustomerRelationshipsMember" xlink:to="lab_us-gaap_CustomerRelationshipsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingIncomeLoss_cba5d12c-71b1-4925-b54a-fd63775f1599_totalLabel_en-US" xlink:label="lab_us-gaap_OperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Operating Income</link:label>
    <link:label id="lab_us-gaap_OperatingIncomeLoss_label_en-US" xlink:label="lab_us-gaap_OperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Income (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingIncomeLoss" xlink:to="lab_us-gaap_OperatingIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditMember_92857630-e3e4-44fb-802e-534302909441_verboseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Revolving Credit Facility, due 2030</link:label>
    <link:label id="lab_us-gaap_LineOfCreditMember_1d2f6948-a106-4e5f-be8b-8fa48eed1f3a_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revolving credit facility</link:label>
    <link:label id="lab_us-gaap_LineOfCreditMember_label_en-US" xlink:label="lab_us-gaap_LineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LineOfCreditMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditMember" xlink:to="lab_us-gaap_LineOfCreditMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_e28d58e1-085f-4740-a657-091e4e764d89_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Retained earnings</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings (Accumulated Deficit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RetainedEarningsAccumulatedDeficit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:to="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfCompensationCostForShareBasedPaymentArrangementsAllocationOfShareBasedCompensationCostsByPlanTableTextBlock_3f029932-d174-4641-8428-b864d8d88814_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfCompensationCostForShareBasedPaymentArrangementsAllocationOfShareBasedCompensationCostsByPlanTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Components of pre-tax stock-based compensation expense</link:label>
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    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_terseLabel_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember"/>
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    <link:label id="lab_us-gaap_TransferredOverTimeMember_d6215f6f-2ecc-4bdc-b0bb-d4c1745e4960_terseLabel_en-US" xlink:label="lab_us-gaap_TransferredOverTimeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Over Time</link:label>
    <link:label id="lab_us-gaap_TransferredOverTimeMember_label_en-US" xlink:label="lab_us-gaap_TransferredOverTimeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Transferred over Time [Member]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TransferredOverTimeMember" xlink:to="lab_us-gaap_TransferredOverTimeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ImpairmentOfIntangibleAssetsIndefinitelivedExcludingGoodwill_9e87987d-8e48-4d22-8dda-138d520016d9_terseLabel_en-US" xlink:label="lab_us-gaap_ImpairmentOfIntangibleAssetsIndefinitelivedExcludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible asset impairment loss</link:label>
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    <link:label id="lab_kai_ScheduleOfItemsIncludedInGainOnSaleAndOtherCostsNetTableTextBlock_753d5653-c4ef-4f33-8544-d7bd5b2d0651_terseLabel_en-US" xlink:label="lab_kai_ScheduleOfItemsIncludedInGainOnSaleAndOtherCostsNetTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of items included in other costs, net</link:label>
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    <link:label id="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember_4906b758-1fd4-419a-b424-48c1aeae6c6f_verboseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Cash Flow Hedges</link:label>
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    <link:label id="lab_us-gaap_SubsequentEventTypeDomain_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsequent Event Type [Domain]</link:label>
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    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationCrossBorderOtherAmount_019bb2ab-b494-7240-ac72-a9b1c07aa26e_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationCrossBorderOtherAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other, effect of cross-border tax laws</link:label>
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    <link:label id="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Grant Date Fair Value of Equity Award Amounts Reported in Summary Compensation Table</link:label>
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    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefit_0531ef25-6d03-4126-a742-6abcf4e650a2_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred income tax provision (benefit)</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefit_281b84cb-992d-44b8-8ab3-db6d0c5df101_totalLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Deferred (benefit) provision</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredIncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_01484bc8-295d-4bc2-9e03-f50f1c09de9a_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustments to reconcile net income to net cash provided by operating activities:</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnrecognizedTaxBenefitsReductionsResultingFromLapseOfApplicableStatuteOfLimitations_3f6dcc86-5f76-4738-b4c6-77c0078e07ab_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_UnrecognizedTaxBenefitsReductionsResultingFromLapseOfApplicableStatuteOfLimitations" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Lapses of Statutes of Limitations</link:label>
    <link:label id="lab_us-gaap_UnrecognizedTaxBenefitsReductionsResultingFromLapseOfApplicableStatuteOfLimitations_label_en-US" xlink:label="lab_us-gaap_UnrecognizedTaxBenefitsReductionsResultingFromLapseOfApplicableStatuteOfLimitations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrecognized Tax Benefits, Reduction Resulting from Lapse of Applicable Statute of Limitations</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrecognizedTaxBenefitsReductionsResultingFromLapseOfApplicableStatuteOfLimitations" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnrecognizedTaxBenefitsReductionsResultingFromLapseOfApplicableStatuteOfLimitations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnrecognizedTaxBenefitsReductionsResultingFromLapseOfApplicableStatuteOfLimitations" xlink:to="lab_us-gaap_UnrecognizedTaxBenefitsReductionsResultingFromLapseOfApplicableStatuteOfLimitations" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_d551a8bc-cb86-4df9-9139-a6e6f35b38f4_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financing Activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ForeignTaxJurisdictionOtherMember_019bb2ab-b494-78ea-8ef6-eec2e6901ce8_terseLabel_en-US" xlink:label="lab_us-gaap_ForeignTaxJurisdictionOtherMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_ForeignTaxJurisdictionOtherMember_label_en-US" xlink:label="lab_us-gaap_ForeignTaxJurisdictionOtherMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Foreign Tax Jurisdiction, Other [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignTaxJurisdictionOtherMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ForeignTaxJurisdictionOtherMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ForeignTaxJurisdictionOtherMember" xlink:to="lab_us-gaap_ForeignTaxJurisdictionOtherMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableRateDomain_e6d6fcc8-f389-4e6c-8afa-028770600129_terseLabel_en-US" xlink:label="lab_us-gaap_VariableRateDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Rate [Domain]</link:label>
    <link:label id="lab_us-gaap_VariableRateDomain_label_en-US" xlink:label="lab_us-gaap_VariableRateDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Rate [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableRateDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VariableRateDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableRateDomain" xlink:to="lab_us-gaap_VariableRateDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerLiability_36d98cb9-10ed-4b9a-99fe-99d7b2eff0e3_terseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contract Liabilities</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerLiability_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract with Customer, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ContractWithCustomerLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerLiability" xlink:to="lab_us-gaap_ContractWithCustomerLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityNoncurrent_c96f1a30-a30f-45fa-880b-149245b074e1_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term obligations</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityNoncurrent_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiabilityNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinanceLeaseLiabilityNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiabilityNoncurrent" xlink:to="lab_us-gaap_FinanceLeaseLiabilityNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllAdjToCompMember_terseLabel_en-US" xlink:label="lab_ecd_AllAdjToCompMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Adjustments to Compensation</link:label>
    <link:label id="lab_ecd_AllAdjToCompMember_label_en-US" xlink:label="lab_ecd_AllAdjToCompMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Adjustments to Compensation [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllAdjToCompMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AllAdjToCompMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllAdjToCompMember" xlink:to="lab_ecd_AllAdjToCompMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AmendmentFlag_d4312033-415f-4102-9ae9-1f22c4c4e110_terseLabel_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:label id="lab_dei_AmendmentFlag_label_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AmendmentFlag" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_AmendmentFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_AmendmentFlag" xlink:to="lab_dei_AmendmentFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_FinanceLeaseCost_6690da16-953b-4cb7-8339-5c96768704fb_totalLabel_en-US" xlink:label="lab_kai_FinanceLeaseCost" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Finance Lease Cost</link:label>
    <link:label id="lab_kai_FinanceLeaseCost_label_en-US" xlink:label="lab_kai_FinanceLeaseCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Cost</link:label>
    <link:label id="lab_kai_FinanceLeaseCost_documentation_en-US" xlink:label="lab_kai_FinanceLeaseCost" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Finance Lease, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_FinanceLeaseCost" xlink:href="kai-20260103.xsd#kai_FinanceLeaseCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_FinanceLeaseCost" xlink:to="lab_kai_FinanceLeaseCost" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_IncreaseDecreaseInEffectiveIncomeTaxRateReconciliationAmountAbstract_cbc9940b-0f78-4091-9664-6233818d97d7_terseLabel_en-US" xlink:label="lab_kai_IncreaseDecreaseInEffectiveIncomeTaxRateReconciliationAmountAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increases (Decreases) Resulting From:</link:label>
    <link:label id="lab_kai_IncreaseDecreaseInEffectiveIncomeTaxRateReconciliationAmountAbstract_label_en-US" xlink:label="lab_kai_IncreaseDecreaseInEffectiveIncomeTaxRateReconciliationAmountAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) In Effective Income Tax Rate Reconciliation, Amount [Abstract]</link:label>
    <link:label id="lab_kai_IncreaseDecreaseInEffectiveIncomeTaxRateReconciliationAmountAbstract_documentation_en-US" xlink:label="lab_kai_IncreaseDecreaseInEffectiveIncomeTaxRateReconciliationAmountAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Increase (Decrease) In Effective Income Tax Rate Reconciliation, Amount [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_IncreaseDecreaseInEffectiveIncomeTaxRateReconciliationAmountAbstract" xlink:href="kai-20260103.xsd#kai_IncreaseDecreaseInEffectiveIncomeTaxRateReconciliationAmountAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_IncreaseDecreaseInEffectiveIncomeTaxRateReconciliationAmountAbstract" xlink:to="lab_kai_IncreaseDecreaseInEffectiveIncomeTaxRateReconciliationAmountAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_A2025AcquisitionsMember_019bb2a8-1e25-7e80-89d5-0890b461b6d8_terseLabel_en-US" xlink:label="lab_kai_A2025AcquisitionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2025 Acquisitions</link:label>
    <link:label id="lab_kai_A2025AcquisitionsMember_label_en-US" xlink:label="lab_kai_A2025AcquisitionsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2025 Acquisitions [Member]</link:label>
    <link:label id="lab_kai_A2025AcquisitionsMember_documentation_en-US" xlink:label="lab_kai_A2025AcquisitionsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2025 Acquisitions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_A2025AcquisitionsMember" xlink:href="kai-20260103.xsd#kai_A2025AcquisitionsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kai_A2025AcquisitionsMember" xlink:to="lab_kai_A2025AcquisitionsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockCommonValue_4b1839c9-bf8d-46db-b7ed-31054a61df8b_negatedLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonValue" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Treasury stock at cost, 2,835,165 and 2,878,080 shares</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonValue_label_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Common, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockCommonValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TreasuryStockCommonValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockCommonValue" xlink:to="lab_us-gaap_TreasuryStockCommonValue" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrTerminationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Termination Date</link:label>
    <link:label id="lab_ecd_TrdArrTerminationDate_label_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Termination Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrTerminationDate" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrTerminationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrTerminationDate" xlink:to="lab_ecd_TrdArrTerminationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInContractWithCustomerAsset_c0836aec-60df-4cd9-9505-d6214bcff6a5_negatedLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInContractWithCustomerAsset" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Contract assets</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInContractWithCustomerAsset_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInContractWithCustomerAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Contract with Customer, Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInContractWithCustomerAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInContractWithCustomerAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInContractWithCustomerAsset" xlink:to="lab_us-gaap_IncreaseDecreaseInContractWithCustomerAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Adopted</link:label>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag_label_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_InsiderTrdPoliciesProcAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:to="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_kai_TimeBasedRestrictedStockUnitsMember_1b2d7818-bc4a-432e-bf0f-cfd3f07983bb_terseLabel_en-US" xlink:label="lab_kai_TimeBasedRestrictedStockUnitsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Time-based restricted stock units</link:label>
    <link:label id="lab_kai_TimeBasedRestrictedStockUnitsMember_label_en-US" xlink:label="lab_kai_TimeBasedRestrictedStockUnitsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Time Based Restricted Stock Units [Member]</link:label>
    <link:label id="lab_kai_TimeBasedRestrictedStockUnitsMember_documentation_en-US" xlink:label="lab_kai_TimeBasedRestrictedStockUnitsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Restricted stock units (RSUs) as awarded by a company to their employees as a form of incentive compensation based on time. Time-based RSU agreement provides for forfeiture in certain events, such as voluntary or involuntary termination of employment, and for acceleration of vesting in certain events, such as death, disability, or a change in control of the entity.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_TimeBasedRestrictedStockUnitsMember" xlink:href="kai-20260103.xsd#kai_TimeBasedRestrictedStockUnitsMember"/>
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    <link:label id="lab_us-gaap_LandAndBuildingMember_647eaacd-b8e5-4c12-9ad8-f68fc8528c54_terseLabel_en-US" xlink:label="lab_us-gaap_LandAndBuildingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Land and Building</link:label>
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    <link:label id="lab_kai_A2024AcquisitionsMember_documentation_en-US" xlink:label="lab_kai_A2024AcquisitionsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2024 Acquisitions</link:label>
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    <link:label id="lab_kai_EmployeeStockPurchasePlanAwardsMember_d89328eb-701d-4e44-8f2c-17e702adfe8b_verboseLabel_en-US" xlink:label="lab_kai_EmployeeStockPurchasePlanAwardsMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Employee stock purchase plan awards</link:label>
    <link:label id="lab_kai_EmployeeStockPurchasePlanAwardsMember_297f7f23-56a7-4b50-9f67-d634b63f6c02_terseLabel_en-US" xlink:label="lab_kai_EmployeeStockPurchasePlanAwardsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Employee Stock Purchase Plan Awards</link:label>
    <link:label id="lab_kai_EmployeeStockPurchasePlanAwardsMember_label_en-US" xlink:label="lab_kai_EmployeeStockPurchasePlanAwardsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Employee Stock Purchase Plan Awards [Member]</link:label>
    <link:label id="lab_kai_EmployeeStockPurchasePlanAwardsMember_documentation_en-US" xlink:label="lab_kai_EmployeeStockPurchasePlanAwardsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Refers to employee stock purchase plan awards.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_EmployeeStockPurchasePlanAwardsMember" xlink:href="kai-20260103.xsd#kai_EmployeeStockPurchasePlanAwardsMember"/>
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    <link:label id="lab_us-gaap_RestructuringAndRelatedActivitiesAbstract_dc961740-a7db-436b-8b69-94f63e77952c_terseLabel_en-US" xlink:label="lab_us-gaap_RestructuringAndRelatedActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restructuring and Related Activities [Abstract]</link:label>
    <link:label id="lab_us-gaap_RestructuringAndRelatedActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_RestructuringAndRelatedActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restructuring and Related Activities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestructuringAndRelatedActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestructuringAndRelatedActivitiesAbstract"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_926174cd-3667-4862-8680-d9867be62b20_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award [Line Items]</link:label>
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    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_ae1147ef-2b00-4d12-92ef-7f6a2e586392_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Common stock, par value (in dollars per share)</link:label>
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    <link:label id="lab_kai_OtherAcquisitionsMember_7dcad092-00e9-40a4-bd43-7ab633894cc2_terseLabel_en-US" xlink:label="lab_kai_OtherAcquisitionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Acquisitions</link:label>
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    <link:label id="lab_kai_OtherAcquisitionsMember_documentation_en-US" xlink:label="lab_kai_OtherAcquisitionsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Acquisitions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kai_OtherAcquisitionsMember" xlink:href="kai-20260103.xsd#kai_OtherAcquisitionsMember"/>
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    <link:label id="lab_us-gaap_UseOfEstimates_56bf4d5d-f89d-4b5c-bb0a-f880fa54aadf_terseLabel_en-US" xlink:label="lab_us-gaap_UseOfEstimates" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Use of Estimates and Critical Accounting Policies</link:label>
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    <link:label id="lab_us-gaap_FinanceLeaseInterestPaymentOnLiability_1aa20158-0560-4b88-9fc7-8a5e16be3440_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseInterestPaymentOnLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating cash flows from finance leases</link:label>
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    <link:label id="lab_us-gaap_ForeignCurrencyContractsLiabilityFairValueDisclosure_204046c1-eafc-4489-a880-91de820dc1a7_terseLabel_en-US" xlink:label="lab_us-gaap_ForeignCurrencyContractsLiabilityFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forward currency-exchange contracts</link:label>
    <link:label id="lab_us-gaap_ForeignCurrencyContractsLiabilityFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_ForeignCurrencyContractsLiabilityFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Foreign Currency Contracts, Liability, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignCurrencyContractsLiabilityFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ForeignCurrencyContractsLiabilityFairValueDisclosure"/>
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    <link:label id="lab_us-gaap_AntidilutiveSecuritiesNameDomain_8552f548-ed49-450b-9e36-d2bd5a7324b8_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesNameDomain_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AntidilutiveSecuritiesNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:to="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfDividendsMinorityInterest_ffe0464b-2d39-4577-9f99-fe4d0fe340c4_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfDividendsMinorityInterest" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Dividends paid to noncontrolling interests</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfDividendsMinorityInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsOfDividendsMinorityInterest"/>
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    <link:label id="lab_us-gaap_LineOfCreditFacilityCommitmentFeePercentage_219f90c1-b030-4756-abb2-4a5f95e24f62_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityCommitmentFeePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitment fee percentage</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityCommitmentFeePercentage_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityCommitmentFeePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Commitment Fee Percentage</link:label>
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    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearFive_896115ff-01c5-4fe9-9eea-b2867baf03ea_terseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearFive_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiabilityPaymentsDueYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability, to be Paid, Year Five</link:label>
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    <link:label id="lab_us-gaap_IntellectualPropertyMember_1cca81f7-2c20-4616-add7-fb7480515c4d_terseLabel_en-US" xlink:label="lab_us-gaap_IntellectualPropertyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product technology</link:label>
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