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          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityEmergingGrowthCompany" xlink:label="dei_EntityEmergingGrowthCompany"/>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Proceeds from Sale of Property, Plant, and Equipment, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Sale of Property, Plant, and Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from the disposal of property and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_AdjustedBalanceOfGoodwillAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Adjusted Balance of Goodwill Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_AdjustedBalanceOfGoodwillAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Adjusted balance of goodwill amount.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_AdjustedBalanceOfGoodwillAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Adjusted balance of goodwill</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAfterTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Cash Flow Hedge, Gain (Loss), before Reclassification, after Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossBeforeReclassificationAfterTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other comprehensive losses before reclassifications</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Present value of lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityIncorporationStateCountryCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Incorporation, State or Country Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability, to be Paid, Year Four</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2030</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Shares Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred stock, shares issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BalanceSheetLocationDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Financial Position Location, Balance [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Asset, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest rate derivative contracts, assets noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilityPaymentsDueYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lease, liability, payments, due year three.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilityPaymentsDueYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease, Liability, Payments, Due Year Three</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilityPaymentsDueYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2029</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Excluding Current Maturities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Long-term debt, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term debt, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Contingent Consideration, Change in Contingent Consideration, Liability, Increase (Decrease)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Contingent consideration and holdbacks payable for acquisitions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PlanNameAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Plan Name [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCurrentReportingStatus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Current Reporting Status</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsBeforeTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), before Reclassifications, before Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsBeforeTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Gain (Loss) Recognized in Other Comprehensive (Loss) Income, before tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ContingentConsiderationRecognizedAmountFromAcquisition_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Contingent Consideration Recognized Amount From Acquisition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ContingentConsiderationRecognizedAmountFromAcquisition_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Contingent consideration recognized amount from acquisition.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ContingentConsiderationRecognizedAmountFromAcquisition_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Contingent consideration recognized amount from acquisition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel2Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Inputs, Level 2 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel2Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Significant Other Observable Inputs (Level 2)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_NonExtendedCommitmentsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Non Extended Commitments [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_NonExtendedCommitmentsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Non-extended commitments.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_NonExtendedCommitmentsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non-Extended Commitments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments and Contingencies Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commitments and Contingencies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashFlowHedgingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Flow Hedging [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashFlowHedgingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash Flow Hedging</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_TwoThousandAndTwentyTwoStockOptionPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two thousand and twenty two stock option plan member.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_TwoThousandAndTwentyTwoStockOptionPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand And Twenty Two Stock Option Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_TwoThousandAndTwentyTwoStockOptionPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2022 Stock Option Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, shares authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares Authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_InterestIncomeAmortizationOfPremium_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amortization of Premium</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_InterestIncomeAmortizationOfPremium_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Income, Amortization Of Premium</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_InterestIncomeAmortizationOfPremium_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Interest income, amortization of premium.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_RelatedPartyPayables_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Payables</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_RelatedPartyPayables_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Related party payables.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_RelatedPartyPayables_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Related party payables</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ProductOrServiceAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Product and Service</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ProductOrServiceAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Product and Service [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalPeriodFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Fiscal Period Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability, to be Paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total lease payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNoncurrentLiabilitiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Noncurrent Liabilities [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNoncurrentLiabilitiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other Long-term Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueFromContractWithCustomerAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revenue from Contract with Customer [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityShellCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Shell Company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Issuances</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of contingent consideration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Cash and Cash Equivalents, at Carrying Value, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash and Cash Equivalent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash and cash equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Maturities of Long-term Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Maturities of Long-Term Debt [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Goodwill</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares, Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Common stock, shares issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares of common stock distributed</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCompensationSharebasedArrangementsLiabilityClassifiedNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Compensation Share-Based Arrangements, Liability, Classified, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCompensationSharebasedArrangementsLiabilityClassifiedNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock option, noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ClassB2AndClassB3UnitMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Class B-2 and class B-3 unit.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ClassB2AndClassB3UnitMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class B-2 and Class B-3 Unit [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ClassB2AndClassB3UnitMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Class B-2 and Class B-3 Unit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedCashNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restricted Cash, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedCashNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Restricted cash included within other assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Right-of-Use Asset Obtained in Exchange for Operating Lease Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease right-of-use assets obtained in exchange for operating lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Grants in Period, Weighted Average Grant Date Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Grant date fair value, stock options</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireBusinessesGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments to Acquire Businesses, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireBusinessesGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Business acquisition, cash consideration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionAcquireeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityFilerCategory_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Filer Category</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities and Equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total liabilities and shareholders' equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeAssetCurrentStatementOfFinancialPositionExtensibleEnumeration_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Asset, Current, Statement of Financial Position [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PayablesAndAccrualsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payables and Accruals [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtCurrent_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Current portion of long-term debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Long-Term Debt, Current Maturities, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Current Maturities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current portion of long-term debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Maturity, Year Three</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2029</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestructuringCostAndReserveAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restructuring Type [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability, to be Paid, Year Three</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2029</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Hedging Relationship [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpensesAndOtherCurrentAssetsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Prepaid Expenses and Other Current Assets [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpensesAndOtherCurrentAssetsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid Expenses and Other Current Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_OtherCreditFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other Credit Facilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_OtherCreditFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Other Credit Facility.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_OtherCreditFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Credit Facility [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_TwoPayFixedReceiveFloatInterestRateSwapContractMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two Pay-Fixed-Receive-Float Interest Rate Swap Contract [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_TwoPayFixedReceiveFloatInterestRateSwapContractMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Pay-Fixed-Receive-Float Interest Rate Swap Contract [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_TwoPayFixedReceiveFloatInterestRateSwapContractMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Two Pay-Fixed-Receive-Float Interest Rate Swap Contract</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ScheduleOfWeightedAverageLeaseTermAndDiscountRateTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Schedule of weighted average lease term and discount rate.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ScheduleOfWeightedAverageLeaseTermAndDiscountRateTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule Of Weighted Average Lease Term And Discount Rate [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ScheduleOfWeightedAverageLeaseTermAndDiscountRateTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Weighted Average Remaining Lease Term and Weighted Average Discount Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LesseeOperatingLeaseLeaseExpectedCommencedTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lessee, operating lease, lease expected commenced, term.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LesseeOperatingLeaseLeaseExpectedCommencedTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Lease Expected Commenced, Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LesseeOperatingLeaseLeaseExpectedCommencedTerm_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease expected commenced term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsValuationAllowance_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Valuation allowance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsValuationAllowance_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Assets, Valuation Allowance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Goodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Goodwill, beginning balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Goodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Goodwill</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Goodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Goodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Goodwill, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Goodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Goodwill, ending balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateContinuingOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Effective Income Tax Rate Reconciliation, Percent, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateContinuingOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateContinuingOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Effective tax rates</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeStockOptionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Stock Options</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability, Current, Statement of Financial Position [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsRemainderOfFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability, to be Paid, Remainder of Fiscal Year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsRemainderOfFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Remainder of 2026</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityIncreaseDecreaseForPeriodNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Line of Credit Facility, Increase (Decrease), Net, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityIncreaseDecreaseForPeriodNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Line of Credit Facility, Increase (Decrease), Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityIncreaseDecreaseForPeriodNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Line of credit facility, increased in borrowing capacity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilityPaymentsDueRemainderOfFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lease liability payments due remainder of fiscal year.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilityPaymentsDueRemainderOfFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease Liability Payments Due Remainder of Fiscal Year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilityPaymentsDueRemainderOfFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Remainder of 2026</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossBeforeTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), before Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossBeforeTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Other Comprehensive Income (Loss), before Tax, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossBeforeTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total Effect on Other Comprehensive (Loss) Income, before tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Additional Paid in Capital, Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Additional paid-in capital</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFinanceCostsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Issuance Costs, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFinanceCostsNet_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Debt issuance costs, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFinanceCostsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt issuance costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock withheld for taxes in net settlement of restricted stock units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Decrease for Tax Withholding Obligation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsRelatedToTaxWithholdingForShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Common stock withheld for taxes in net settlement of restricted stock units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Related Party</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_OriginalIssueDiscountAndDebtIssuanceInitialIncurredCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Original issue discount and debt issuance costs initial costs incurred</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_OriginalIssueDiscountAndDebtIssuanceInitialIncurredCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Original Issue Discount and Debt Issuance Initial Incurred Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_OriginalIssueDiscountAndDebtIssuanceInitialIncurredCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Original issue discount and debt issuance initial incurred costs.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentVariableInterestRateTypeExtensibleEnumeration_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment, Variable Interest Rate, Type [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardTermsOfAward_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Plan term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardTermsOfAward_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Terms of Award</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VestingDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Vesting [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Grants in Period, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Options granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisaggregationOfRevenueTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disaggregation of Revenue [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Earnings Per Share, Basic and Diluted [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Reconciliations of Basic and Diluted Net (Loss) Income per Common Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ClassB2UnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Class B2 Units.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ClassB2UnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class B2 Units [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ClassB2UnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Class B-2 Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Earnings Per Share, Basic, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share, Basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisaggregationOfRevenueTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disaggregation of Revenue [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisaggregationOfRevenueTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Total Revenue Between Education Centers and School Sites</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAccountsPayableAndAccruedLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Accounts Payable and Accrued Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAccountsPayableAndAccruedLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_KcParentLpAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">KC Parent, LP Agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_KcParentLpAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">KC Parent, LP Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_KcParentLpAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">KC Parent, LP Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_KcParentLpAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">KC Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ImpairmentOfLeasehold_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Impairment of Leasehold</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ImpairmentOfLeasehold_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Impairment of lease right-of-use assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total current liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GovernmentAssistanceAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Government Assistance [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Accounts Receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsReceivable_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Accounts receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Adjustments to reconcile net (loss) income to cash provided by operating activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_IncreaseDecreaseInLeases_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Increase (decrease) in leases.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_IncreaseDecreaseInLeases_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_IncreaseDecreaseInLeases_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Changes of the Fair Value of Recurring Level 3 Fair Value Measurements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ClassAUnitMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Class A Unit.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ClassAUnitMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class A Unit [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ClassAUnitMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Class A Unit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfDebtIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Payments of debt issuance costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfDebtIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments of Debt Issuance Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfDebtIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt issuance costs, incurred</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity, Attributable to Parent [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shareholders' equity:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntitySmallBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Small Business</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_FinanceLeaseCostAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Finance lease cost.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_FinanceLeaseCostAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease Cost [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_FinanceLeaseCostAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Finance lease expense:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Retained Earnings (Accumulated Deficit), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Retained Earnings (Accumulated Deficit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Retained deficit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsidiary or Equity Method Investee, Sale of Stock, Type [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GrantsReceivableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Grants Receivable, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GrantsReceivableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Grants receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeInceptionDates_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative, Inception Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeInceptionDates_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivative commencement date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_FinanceLeaseLiabilityPaymentsDueAfterYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Finance lease liability payments due after year four.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_FinanceLeaseLiabilityPaymentsDueAfterYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease Liability Payments Due After Year Four</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_FinanceLeaseLiabilityPaymentsDueAfterYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Thereafter</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TypeOfCostGoodOrServiceExtensibleList_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cost, Product and Service [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostOfGoodsAndServicesSoldDepreciationAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Cost, Depreciation and Amortization, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostOfGoodsAndServicesSoldDepreciationAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cost, Depreciation and Amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostOfGoodsAndServicesSoldDepreciationAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Depreciation and amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnconditionalPurchaseObligationCategoryOfGoodsOrServicesAcquiredDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Unconditional Purchase Obligation, Category of Goods or Services Acquired [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ReimbursementOfFoodCost_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Reimbursement of food cost.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ReimbursementOfFoodCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Reimbursement Of Food Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ReimbursementOfFoodCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Food subsidies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeasesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Leases [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonClassAMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Class A [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonClassAMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Class A Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Effect of dilutive securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Weighted Average Number of Shares Outstanding, Diluted, Adjustment, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Number of Shares Outstanding, Diluted, Adjustment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeLeaseDescriptionLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Lease, Description [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostOfGoodsAndServiceExcludingDepreciationDepletionAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Cost of Goods and Service, Excluding Depreciation, Depletion, and Amortization, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostOfGoodsAndServiceExcludingDepreciationDepletionAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cost of Goods and Service, Excluding Depreciation, Depletion, and Amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostOfGoodsAndServiceExcludingDepreciationDepletionAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cost of services (excluding depreciation and impairment)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AmendmentFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amendment Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ProductsAndServicesDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Product and Service [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ProductsAndServicesDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Product and Service</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseInterestExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Interest Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseInterestExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest on lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities and Equity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Liabilities and Shareholders' Equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ClassA1UnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class A1 Units [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ClassA1UnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Class A-1 Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ClassA1UnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Class A1 Units.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressPostalZipCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, Postal Zip Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Cash provided by operating activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingCodmProfitLossMeasureHowUsedDescription_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting, CODM, Profit (Loss) Measure, How Used, Description</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeLiabilityNoncurrentStatementOfFinancialPositionExtensibleEnumeration_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Liability, Noncurrent, Statement of Financial Position [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Maturity, Year One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2027</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangements by Share-Based Payment Award, Options, Grants in Period, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Exercise price of options</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HedgingRelationshipDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Hedging Relationship [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Year Three</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2029</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated depreciation, property and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentInterestRateEffectivePercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt instrument effective interest rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentInterestRateEffectivePercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Interest Rate, Effective Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressAddressLine1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, Address Line One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxesAndTaxCredits_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Income Taxes and Tax Credits</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxesAndTaxCredits_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Deferred Income Taxes and Tax Credits, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxesAndTaxCredits_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Change in deferred taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Hierarchy and NAV [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net income per common share:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Net (loss) income per common share:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_DerivativeVariableRateDescription_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Variable Rate Description</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_DerivativeVariableRateDescription_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Derivative variable rate description.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_DerivativeVariableRateDescription_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivative variable rate description</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SupplementalCashFlowInformationAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Supplemental Cash Flow Information [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SupplementalCashFlowInformationAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Supplemental cash flow information:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ReductionsToFinanceLeaseRightOfUseAssetsResultingFromReductionsToFinanceLeaseLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Reductions to finance lease right-of-use assets resulting from reductions to finance lease liabilities.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ReductionsToFinanceLeaseRightOfUseAssetsResultingFromReductionsToFinanceLeaseLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Reductions To Finance Lease Right-of-use Assets Resulting From Reductions To Finance Lease Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ReductionsToFinanceLeaseRightOfUseAssetsResultingFromReductionsToFinanceLeaseLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Reductions to finance lease right-of-use assets resulting from reductions to finance lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BalanceSheetLocationAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Financial Position Location, Balance [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Right-of-Use Asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease right-of-use assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Less imputed interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityUndiscountedExcessAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability, Undiscounted Excess Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodBeforeTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Reclassification from Accumulated Other Comprehensive Income, Current Period, before Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodBeforeTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Loss (Gain) Reclassified from Accumulated Other Comprehensive (Loss) Income into Earnings, before tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentType_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxesPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Income Taxes Paid, Net, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxesPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Taxes Paid, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxesPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash paid for income taxes, net of refunds</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCentralIndexKey_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Central Index Key</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCentralIndexKey_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Central Index Key</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Period Increase (Decrease), Including Exchange Rate Effect and Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net change in cash, cash equivalents, and restricted cash</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilityPaymentsDueYearTwo_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lease, liability, payments, due year two.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilityPaymentsDueYearTwo_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease, Liability, Payments, Due Year Two</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilityPaymentsDueYearTwo_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2028</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event Type [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_Rule10B51ArrangementModifiedFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Rule 10b5-1 Arrangement Modified [Flag]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_Rule10B51ArrangementModifiedFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Rule 10b5-1 arrangement modified.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_Rule10B51ArrangementModifiedFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Rule 10b5-1 Arrangement Modified</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationConsiderationTransferredOther1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Consideration Transferred, Tangible and Intangible Assets, Excluding Cash</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationConsiderationTransferredOther1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Contingent consideration transferred</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities Excluded from Computation of Earnings Per Share, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Antidilutive shares excluded from calculation of diluted net income per common share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_Share-BasedCompensationArrangementByShare-BasedPaymentAwardIncreaseInNumberOfSharesAvailableForGrant_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Increase In Number of Shares Available for Grant</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_Share-BasedCompensationArrangementByShare-BasedPaymentAwardIncreaseInNumberOfSharesAvailableForGrant_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share-based compensation arrangement by share-based payment award, increase in number of shares available for grant.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_Share-BasedCompensationArrangementByShare-BasedPaymentAwardIncreaseInNumberOfSharesAvailableForGrant_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Aggregate number of shares increased</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Par or Stated Value Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, par value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationAwardTrancheOneMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Tranche One [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationAwardTrancheOneMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">25% on First Anniversary of Grant Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_NoncashOperatingReclassificationOfEquityClassifiedStockOptionsAndRestrictedStockUnitsToLiabilityClassified_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Reclassification of equity-classified stock options and restricted stock units to liability-classified</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_NoncashOperatingReclassificationOfEquityClassifiedStockOptionsAndRestrictedStockUnitsToLiabilityClassified_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Noncash operating reclassification of equity-classified stock options and restricted stock units to liability-classified.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_NoncashOperatingReclassificationOfEquityClassifiedStockOptionsAndRestrictedStockUnitsToLiabilityClassified_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Noncash Operating Reclassification Of Equity-classified Stock Options And Restricted Stock Units To Liability-classified</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationAndTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Other Comprehensive Income (Loss), Cash Flow Hedge, Gain (Loss), after Reclassification and Tax, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationAndTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Cash Flow Hedge, Gain (Loss), after Reclassification and Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationAndTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Change in net gains (losses) on cash flow hedges</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Reclassification out of Accumulated Other Comprehensive Income [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeNotionalAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative, Notional Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeNotionalAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Notional amount of derivative instrument</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock upon settlement of restricted stock units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueRestrictedStockAwardGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Value, Restricted Stock Award, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CurrentFiscalYearEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Current Fiscal Year End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Long-Term Debt Instruments [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentQuarterlyReport_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Quarterly Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_LitigationCaseTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Litigation Case [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByBalanceSheetGroupingTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, by Balance Sheet Grouping [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressStateOrProvince_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, State or Province</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_NumberOfLeasedCenterSitesImpactedByLeaseAmendment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number of Leased Center Sites Impacted by Lease Amendment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_NumberOfLeasedCenterSitesImpactedByLeaseAmendment_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Number of leased center sites impacted by lease amendment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_NumberOfLeasedCenterSitesImpactedByLeaseAmendment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of leased center sites impacted by lease amendment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Line of Credit Facility, Remaining Borrowing Capacity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Remaining borrowing capacity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Line of credit facility, remaining borrowing capacity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardPlanModificationNumberOfEmployeesAffected_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of participants impacted by the plan modification</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardPlanModificationNumberOfEmployeesAffected_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Plan Modification, Number of Grantees Affected</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Shares Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Preferred Stock, Shares Outstanding, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Preferred Stock, Shares Outstanding, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred stock, shares outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Comprehensive Income (Loss), Net of Tax, Attributable to Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total comprehensive (loss) income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ContractWithCustomerLiabilityRevenueRecognized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Contract with Customer, Liability, Revenue Recognized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ContractWithCustomerLiabilityRevenueRecognized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred revenue, revenue recognized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock withheld for taxes in net settlement of restricted stock units, Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Shares Withheld for Tax Withholding Obligation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesPaidForTaxWithholdingForShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Common stock withheld for taxes in net settlement of restricted stock units, Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_CashSettledRestrictedStockUnitsLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cash settled restricted stock units liabilities.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_CashSettledRestrictedStockUnitsLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Settled Restricted Stock Units Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_CashSettledRestrictedStockUnitsLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash settled RSU liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_RelatedPartyTransactionRelatedPartiesRent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Related party transaction, related parties rent.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_RelatedPartyTransactionRelatedPartiesRent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transaction, Related Parties Rent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_RelatedPartyTransactionRelatedPartiesRent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Related parties rent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInDueToRelatedPartiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Increase (Decrease) in Due to Related Parties, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInDueToRelatedPartiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Due to Related Parties, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInDueToRelatedPartiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Related party payables</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ExtendedAndNonExtendedCommitmentsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Extended and Non-Extended Commitments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ExtendedAndNonExtendedCommitmentsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Extended and Non Extended Commitments [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ExtendedAndNonExtendedCommitmentsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Extended and non extended commitments.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilityPaymentsDue_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lease, liability, payments, due.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilityPaymentsDue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease, Liability, Payments, Due</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilityPaymentsDue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total lease payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Net of Tax [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other comprehensive (loss) income, net of tax:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_IndependentBoardMembersMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Independent Board Members</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_IndependentBoardMembersMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Independent board members member.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_IndependentBoardMembersMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Independent Board Members [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Estimated fair value of first lien term loans</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Subsequent Event</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilityUndiscountedExcessAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Less imputed interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilityUndiscountedExcessAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lease, liability, undiscounted excess amount.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilityUndiscountedExcessAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease, Liability, Undiscounted Excess Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Maturity, Remainder of Fiscal Year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalRemainderOfFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Remainder of 2026</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Reclassification from Accumulated Other Comprehensive Income, Current Period, Net of Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">(Gain) loss reclassified from accumulated other comprehensive (loss) income into income, netof taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Loss (Gain) Reclassified from Accumulated Other Comprehensive (Loss) Income into (Loss) Income, net of taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_SubsidyRevenueMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Subsidy Revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_SubsidyRevenueMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Subsidy revenue.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_SubsidyRevenueMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsidy Revenue [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredRevenueCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Deferred Revenue, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredRevenueCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Revenue, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredRevenueCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Assets, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_OperatingAndFinanceLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Operating and finance lease right of use asset.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_OperatingAndFinanceLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating And Finance Lease Right Of Use Asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_OperatingAndFinanceLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total lease right-of-use assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Award Vesting Rights, Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Vesting percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ImpairmentLosses_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Impairment Losses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ImpairmentLosses_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Impairment losses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ImpairmentLosses_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Impairment losses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transaction [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated Other Comprehensive (Loss) Income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">AOCI Attributable to Parent [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillImpairmentLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill, Impairment Loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillImpairmentLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Impairment of goodwill</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillImpairmentLoss_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Impairment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationConsiderationTransferred1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Business acquisition, total consideration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationConsiderationTransferred1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Consideration Transferred</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationConsiderationTransferred1_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Business Combination, Consideration Transferred, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Value, Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred stock, par value $0.01; 25,000 shares authorized; no shares issued and outstanding as of April 4, 2026 and January 3, 2026</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_NonRule10B51ArrangementModifiedFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Non-Rule 10b5-1 Arrangement Modified [Flag]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_NonRule10B51ArrangementModifiedFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Non-Rule 10b5-1 arrangement modified.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_NonRule10B51ArrangementModifiedFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non-Rule 10b5-1 Arrangement Modified</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Selling, General and Administrative Expense, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Selling, General and Administrative Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Selling, general, and administrative expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Reclassification out of Accumulated Other Comprehensive Income [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_Covid19RelatedStimulusMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">COVID-19 Related Stimulus Member.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_Covid19RelatedStimulusMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">COVID-19 Related Stimulus [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_Covid19RelatedStimulusMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">COVID-19 Related Stimulus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MinimumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Minimum [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MinimumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Minimum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">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:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted Average Grant Date Fair Value, Granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Grant date fair value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancialInstrumentAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financial Instrument [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current assets:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Other Comprehensive Income (Loss), Tax, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total effect on other comprehensive Loss, tax effect</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossTax_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Total Effect on Other Comprehensive (Loss) Income, tax effect</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonClassBMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Class B [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonClassBMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Class B Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel3Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Inputs, Level 3 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel3Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Significant Unobservable Inputs (Level 3)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_EmployeeRetentionCreditsReceivableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Employee Retention Credits Receivable Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_EmployeeRetentionCreditsReceivableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Employee retention credits receivable current.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accumulated Gain (Loss), Net, Cash Flow Hedge, Parent [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated Gain (Loss), Net, Cash Flow Hedge, Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lease agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Lease Agreements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current liabilities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities, Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Liabilities-current:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transactions [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Ending Balance, Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Beginning Balance, Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Shares, Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Accounts Receivable, after Allowance for Credit Loss, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Receivable, after Allowance for Credit Loss, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsReceivableNetCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts receivable, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingencies_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments and Contingencies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingencies_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commitments and contingencies (Note 13)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareholdersEquityAndShareBasedPaymentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Shareholders' Equity and Share-Based Payments [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareholdersEquityAndShareBasedPaymentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock-Based Compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_IssuanceOfCommonStockThroughNetSettlementOfRestrictedStockUnits_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock through net settlement of restricted stock units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_IssuanceOfCommonStockThroughNetSettlementOfRestrictedStockUnits_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Issuance of common stock through net settlement of restricted stock units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_IssuanceOfCommonStockThroughNetSettlementOfRestrictedStockUnits_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Issuance of common stock through net settlement of restricted stock units.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Present value of lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Basis Spread on Variable Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Variable interest rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ScenarioForecastMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Forecast [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ScenarioForecastMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Forecast</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfGoodwillTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Changes in Carrying Amount of Goodwill</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfGoodwillTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Goodwill [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Maturity, Year Two</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearTwo_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2028</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Finance lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Less current portion of lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financing lease obligations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeLeaseDescriptionTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Lease, Description [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted average discount rate (Finance)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Weighted Average Discount Rate, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CapitalExpendituresIncurredButNotYetPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property and equipment additions included in accounts payable and accrued liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CapitalExpendituresIncurredButNotYetPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Capital Expenditures Incurred but Not yet Paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongtermDebtTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Type [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Weighted Average Number of Shares Outstanding, Basic, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Number of Shares Outstanding, Basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted average number of common shares outstanding, basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillAcquiredDuringPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill, Acquired During Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillAcquiredDuringPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Additions from acquisitions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_StatementScenarioAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Scenario [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_OutstandingBalanceOfLettersOfCreditRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Outstanding Balance Of Letters Of Credit Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_OutstandingBalanceOfLettersOfCreditRate_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Outstanding balance of letters of credit rate.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_OutstandingBalanceOfLettersOfCreditRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Outstanding balance of letters of credit rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOtherCurrentLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Other Current Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOtherCurrentLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other current liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ReimbursementsOfInterestIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Reimbursements Of Interest Income.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ReimbursementsOfInterestIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Reimbursements Of Interest Income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ReimbursementsOfInterestIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Reimbursements of interest income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_RelatedPartyTransactionPartnersGroupManagementServices_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Partners Group management services</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_RelatedPartyTransactionPartnersGroupManagementServices_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Related party transaction, partners group management services.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_RelatedPartyTransactionPartnersGroupManagementServices_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transaction, Partners Group Management Services</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Share-Based Compensation Arrangements by Share-Based Payment Award [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Right-of-Use Asset, Statement of Financial Position [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Subsequent Events</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Events [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transactions Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Related Party Transactions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">APIC, Share-Based Payment Arrangement, Increase for Cost Recognition, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">APIC, Share-Based Payment Arrangement, Increase for Cost Recognition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock-based compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity, Attributable to Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total shareholders' equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireInvestments_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Payments to Acquire Investments, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireInvestments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments to Acquire Investments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireInvestments_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Investments in deferred compensation asset trusts</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Par or Stated Value Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred stock, par value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_SeniorSecuredCreditFacilitiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Senior Secured Credit Facilities.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_SeniorSecuredCreditFacilitiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Senior Secured Credit Facilities [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_SeniorSecuredCreditFacilitiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Senior Secured Credit Facilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BasisOfAccountingPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Basis of Accounting, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BasisOfAccountingPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Basis of Presentation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfStockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Stockholders' Equity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationAwardTrancheTwoMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Tranche Two [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationAwardTrancheTwoMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Remaining Following First Anniversary of Grant Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss) before Reclassifications, Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Other Comprehensive Income (Loss) before Reclassifications, Tax, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income tax effect</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsTax_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Gain (Loss) Recognized in Other Comprehensive (Loss) Income, tax effects</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TypeOfRestructuringDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Type of Restructuring [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Disclosures [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value Measurements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_FirstLienTermLoanFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">First Lien Term Loan Facility</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_FirstLienTermLoanFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">First lien term loan facility.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_FirstLienTermLoanFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">First Lien Term Loan Facility [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_FirstLienTermLoanFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">First Lien Term Loans</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NoncashInvestingAndFinancingItemsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Noncash Investing and Financing Items [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NoncashInvestingAndFinancingItemsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non-cash investing and financing activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Maturity, Year Four</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtMaturitiesRepaymentsOfPrincipalInYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2030</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_EmployeeRetentionCreditsReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Employee Retention Credits Receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_EmployeeRetentionCreditsReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Employee retention credits receivable.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_EmployeeRetentionCreditsReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Employee retention credits receivable, non-current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Instruments and Hedging Activities Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingCodmIndividualTitleAndPositionOrGroupOrCommitteeNameExtensibleEnumeration_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting, CODM, Individual Title and Position or Group Name [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PlanNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Plan Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOtherOperatingAssets_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Other assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOtherOperatingAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Increase (Decrease) in Other Operating Assets, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOtherOperatingAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Other Operating Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MutualFundMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Mutual Fund [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MutualFundMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Mutual Fund</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CreditFacilityAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Credit Facility [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_CivilActionSettlementAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Civil Action Settlement Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_CivilActionSettlementAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Civil action settlement agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_CivilActionSettlementAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Civil Action Settlement Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ImpairmentOfLongLivedAssetsHeldForUse_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Impairment, Long-Lived Asset, Held-for-Use, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ImpairmentOfLongLivedAssetsHeldForUse_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Impairment, Long-Lived Asset, Held-for-Use</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ImpairmentOfLongLivedAssetsHeldForUse_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Impairment of property and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability, to be Paid, Year One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2027</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingRights_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Award Vesting Rights</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingRights_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Vesting description</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating Leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Fiscal Year Maturity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related and Nonrelated Parties [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GovernmentAssistanceTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Government Assistance [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Less current portion of lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lease, liability, current.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease, Liability, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressCityOrTown_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, City or Town</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfReportableSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number of Reportable Segments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfReportableSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of reportable segments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_SecurityExchangeName_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Security Exchange Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtIssuanceCostsIncurredDuringNoncashOrPartialNoncashTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt issuance costs incurred</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtIssuanceCostsIncurredDuringNoncashOrPartialNoncashTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Issuance Costs Incurred During Noncash or Partial Noncash Transaction</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CreditFacilityDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Credit Facility [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentVariableInterestRateTypeExtensibleEnumeration_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Variable Interest Rate, Type [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Term loan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Term loans</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LesseeOperatingLeaseLeaseNotYetCommencedAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lessee, operating lease, lease not yet commenced, amount.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LesseeOperatingLeaseLeaseNotYetCommencedAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Lease Not Yet Commenced, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LesseeOperatingLeaseLeaseNotYetCommencedAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease not yet commenced</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityBankruptcyProceedingsReportingCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Bankruptcy Proceedings, Reporting Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_InitialPremiumOfInterestRateCap_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Initial Premium of Interest Rate Cap</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_InitialPremiumOfInterestRateCap_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Initial premium of interest rate cap.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_InitialPremiumOfInterestRateCap_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Initial premium of interest rate cap</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">(Loss) income before income taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_NumberOfChildrenWithLicenseCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Number of children with license capacity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_NumberOfChildrenWithLicenseCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number of Children With License Capacity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_NumberOfChildrenWithLicenseCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of children with license capacity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities, Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lease, liability, payments, due next twelve months.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease, Liability, Payments, Due Next Twelve Months</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2027</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Cash, cash equivalents, and restricted cash at beginning of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Cash, cash equivalents, and restricted cash at end of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Continuing Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total cash, cash equivalents, and restricted cash at end of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash paid for interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Paid, Excluding Capitalized Interest, Operating Activity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statistical Measurement [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllocatedShareBasedCompensationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Allocated shared based compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllocatedShareBasedCompensationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentPeriodEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Period End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_TitleOfIndividualAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Title and Position [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementsFairValueHierarchyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Hierarchy and NAV [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilityPaymentsDueAfterYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Thereafter</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilityPaymentsDueAfterYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lease liability payments due after year four.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilityPaymentsDueAfterYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease Liability Payments Due After Year Four</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityCommitmentFeePercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Line of Credit Facility, Commitment Fee Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityCommitmentFeePercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Letters of credit fee interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityCommitmentFeePercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Line of credit facility, commitment fee percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnSaleOfPropertyPlantEquipment_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Gain on disposal of property and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnSaleOfPropertyPlantEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Gain (Loss) on Disposition of Property Plant Equipment, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnSaleOfPropertyPlantEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gain (Loss) on Disposition of Property Plant Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_TwoThousandAndTwentyTwoIncentiveAwardPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2022 Incentive Award Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_TwoThousandAndTwentyTwoIncentiveAwardPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two thousand and twenty two incentive award plan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_TwoThousandAndTwentyTwoIncentiveAwardPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand And Twenty Two Incentive Award Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityNoncurrentStatementOfFinancialPositionExtensibleList_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability, Noncurrent, Statement of Financial Position [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_BeforeAndAfterSchoolSitesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Before and after school sites.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_BeforeAndAfterSchoolSitesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Before And After School Sites [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_BeforeAndAfterSchoolSitesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Before- and After-School Sites</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfFinancialPositionAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Financial Position [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedStockUnitsRSUMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restricted Stock Units (RSUs) [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedStockUnitsRSUMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">RSUs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilitiesCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lease liabilities current.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilitiesCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease Liabilities Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilitiesCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Liabilities-current:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VestingAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Vesting [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Reclassification out of Accumulated Other Comprehensive Income [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total Effect on Other Comprehensive Income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Reconciliation of cash, cash equivalents, and restricted cash to the unaudited condensed consolidated balance sheets:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Continuing Operation [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementClassOfStockAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Stock [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_TwoThousandAndTwentyTwoRestrictedStockUnitsPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two thousand and twenty two restricted stock units plan member.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_TwoThousandAndTwentyTwoRestrictedStockUnitsPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand And Twenty Two Restricted Stock Units Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_TwoThousandAndTwentyTwoRestrictedStockUnitsPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2022 RSUs Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLeaseNotYetCommencedMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Lease Not yet Commenced [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLeaseNotYetCommencedMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating Lease, Lease Not yet Commenced</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Thereafter</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Long term debt maturities repayments of principal after year four.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long Term Debt Maturities Repayments Of Principal After Year Four</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilitiesPaymentsDueAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability, to be Paid, Fiscal Year Maturity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilitiesPaymentsDueAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Finance Leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Liabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Liabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_NumberOfCommunityBasedAndEmployerSponsoredEarlyChildhoodEducationAndCareServicesCenters_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Number of community based and employer sponsored early childhood education and care services centers.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_NumberOfCommunityBasedAndEmployerSponsoredEarlyChildhoodEducationAndCareServicesCenters_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number Of Community Based And Employer Sponsored Early Childhood Education And Care Services Centers</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_NumberOfCommunityBasedAndEmployerSponsoredEarlyChildhoodEducationAndCareServicesCenters_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of community-based and employer-sponsored early childhood education and care services centers</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financial Instruments [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_CommonStockConvertibleConversionRatio_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Common stock convertible conversion ratio.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_CommonStockConvertibleConversionRatio_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock Convertible Conversion Ratio</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_CommonStockConvertibleConversionRatio_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, convertible ratio</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInDeferredRevenue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Deferred Revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInDeferredRevenue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardRequisiteServicePeriod1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Award Requisite Service Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardRequisiteServicePeriod1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Award requisite service period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Year Two</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2028</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseRightOfUseAssetAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Right-of-Use Asset, Amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseRightOfUseAssetAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amortization of right-of-use assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GovernmentAssistanceTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Government Assistance, Type [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_TaxPaymentsRelatedToNetSettlementOfRestrictedStockUnits_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Tax payments related to net settlement of restricted stock units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_TaxPaymentsRelatedToNetSettlementOfRestrictedStockUnits_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tax Payments Related to Net Settlement of Restricted Stock Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_TaxPaymentsRelatedToNetSettlementOfRestrictedStockUnits_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tax payments related to net settlement of restricted stock units.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Number of Shares Outstanding, Diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted average number of common shares outstanding, diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Weighted average number of common shares outstanding, diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GovernmentAssistanceTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Government Assistance [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GovernmentAssistanceTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Government Assistance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityFileNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity File Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Other Assets, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Due from unconsolidated related parties</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CoverAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cover [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_BusinessCombinationConsiderationHoldbacks_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination Consideration Holdbacks</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_BusinessCombinationConsiderationHoldbacks_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Business combination consideration holdbacks.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_BusinessCombinationConsiderationHoldbacks_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Business acquisition, holdbacks</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts payable and accrued liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Increase (Decrease) in Accounts Payable and Accrued Liabilities, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Accounts Payable and Accrued Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_RestrictedStockUnitsAndStockOptionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restricted Stock Units And Stock Options [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_RestrictedStockUnitsAndStockOptionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Restricted stock units and stock options.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_RestrictedStockUnitsAndStockOptionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock Options and RSUs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Prepaid Expense and Other Assets, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total prepaid expenses and other current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid expenses and other current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TaxesPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Taxes Payable, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TaxesPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Taxes Payable, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TaxesPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued property and other taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ReclassificationFromAociCurrentPeriodTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Reclassification from AOCI, Current Period, Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ReclassificationFromAociCurrentPeriodTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Reclassification from AOCI, Current Period, Tax, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ReclassificationFromAociCurrentPeriodTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">(Gain) loss reclassified from accumulated other comprehensive (loss) income into income, tax effect</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ReclassificationFromAociCurrentPeriodTax_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Loss (Gain) Reclassified from Accumulated Other Comprehensive (Loss) Income into Earnings, tax effect</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ScenarioUnspecifiedDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Scenario [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_FairValueOfContingentConsiderationAmountPayableTermFromAcquisitionDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value of Contingent Consideration Amount Payable Term From Acquisition Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_FairValueOfContingentConsiderationAmountPayableTermFromAcquisitionDate_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Fair value of contingent consideration amount payable term from acquisition date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_FairValueOfContingentConsiderationAmountPayableTermFromAcquisitionDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair value of contingent consideration amount payable term from acquisition date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_DerivativeCommencementDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Commencement Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_DerivativeCommencementDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivative, commencement date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_DerivativeCommencementDate_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Derivative commencement date.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfOperatingSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of consolidated segments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfOperatingSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number of Operating Segments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Segment Information</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestRateCashFlowHedgeGainLossToBeReclassifiedDuringNext12MonthsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Rate Cash Flow Hedge Gain (Loss) to be Reclassified During Next 12 Months, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestRateCashFlowHedgeGainLossToBeReclassifiedDuringNext12MonthsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred loss recognized within accumulated other comprehensive loss reclassified as decrease in interest expense within the next twelve months</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityInterestRateDuringPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Line of Credit Facility, Interest Rate During Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityInterestRateDuringPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Line of credit facility outstanding balance percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gain (Loss) on Extinguishment of Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Gain (loss) on extinguishment of debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Gain (Loss) on Extinguishment of Debt, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Loss on extinguishment of long-term debt, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainsLossesOnExtinguishmentOfDebt_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Loss on extinguishment of long-term debt, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentInterestRateIncreaseDecrease_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Interest Rate, Increase (Decrease)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentInterestRateIncreaseDecrease_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Decrease in interest rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_AdjustmentsToAdditionalPaidInCapitalDistributionToKcParent_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Distribution to KC Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_AdjustmentsToAdditionalPaidInCapitalDistributionToKcParent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Adjustments To Additional Paid In Capital, Distribution To Kc Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_AdjustmentsToAdditionalPaidInCapitalDistributionToKcParent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Adjustments to additional paid in capital, distribution to kc parent.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Recently Issued Accounting Pronouncements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">New Accounting Pronouncements, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Award Vesting Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Vesting period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNoteTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Comprehensive Income (Loss) Note [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNoteTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated Other Comprehensive (Loss) Income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfLongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Proceeds from Issuance of Long-Term Debt, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfLongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Issuance of Long-Term Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfLongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from issuance of long-term debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Nonvested Award, Excluding Option, Cost Not yet Recognized, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedShareBasedAwardsOtherThanOptions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unrecognized stock-based compensation expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_NonCashOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Non-cash operating activities.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_NonCashOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Non-cash Operating Activities [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_NonCashOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non-cash operating activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureAndSignificantAccountingPoliciesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Organization, Consolidation and Presentation of Financial Statements Disclosure and Significant Accounting Policies [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureAndSignificantAccountingPoliciesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Organization and Summary of Significant Accounting Policies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Common Stock, Shares, Outstanding, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Common Stock, Shares, Outstanding, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares, Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Common stock, shares outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease liabilities-current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Operating lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Less current portion of lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationDepletionAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Depreciation, Depletion and Amortization, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationDepletionAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Depreciation, Depletion and Amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepreciationDepletionAndAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Depreciation and amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentTransitionReport_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Transition Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_EarlyChildhoodEducationCentersMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Early childhood education centers.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_EarlyChildhoodEducationCentersMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Early Childhood Education Centers [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_EarlyChildhoodEducationCentersMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Early Childhood Education Centers</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecordedUnconditionalPurchaseObligationByCategoryOfItemPurchasedAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Unrecorded Unconditional Purchase Obligation by Category of Item Purchased [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetImpairmentCharges_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Impairment Charges</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetImpairmentCharges_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total impairment losses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetImpairmentCharges_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Impairment losses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetImpairmentCharges_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total impairment losses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfCashFlowsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Cash Flows [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireBusinessesNetOfCashAcquired_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Payments to Acquire Businesses, Net of Cash Acquired, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireBusinessesNetOfCashAcquired_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments to Acquire Businesses, Net of Cash Acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireBusinessesNetOfCashAcquired_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Payments for acquisitions, net of cash acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestRateSwapMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest Rate Swap</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestRateSwapMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Rate Swap [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net (Loss) Income per Common Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ScheduleOfRightOfUseAssetsAndLeaseLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Right-of-Use Assets and Lease Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ScheduleOfRightOfUseAssetsAndLeaseLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Schedule of right of use assets and lease liabilities.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ScheduleOfRightOfUseAssetsAndLeaseLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule Of Right Of Use Assets And Lease Liabilities [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Net (loss) income available to common shareholders, basic and diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net (loss) income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GovernmentAssistanceLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Government Assistance [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_OperatingAndFinanceLeaseLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Operating and finance lease liabilities.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_OperatingAndFinanceLeaseLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating And Finance Lease Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_OperatingAndFinanceLeaseLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LineOfCreditFacilityFrontingFeePercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fronting fee percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LineOfCreditFacilityFrontingFeePercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Line of credit facility, fronting fee percentage.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LineOfCreditFacilityFrontingFeePercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Line Of Credit Facility, Fronting Fee Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfDistributionsToAffiliates_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments of Distributions to Affiliates</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfDistributionsToAffiliates_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Distribution to KC Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfDistributionsToAffiliates_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Distribution to parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasicLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share, Basic, by Common Class, Including Two Class Method [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_AdjustmentsToAdditionalPaidInCapitalDistributionToParent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Adjustments To Additional Paid In Capital Distribution To Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_AdjustmentsToAdditionalPaidInCapitalDistributionToParent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Adjustments to additional paid in capital distribution to parent.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_AdjustmentsToAdditionalPaidInCapitalDistributionToParent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Distribution to parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilityPaymentsDueYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lease, liability, payments, due year four.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilityPaymentsDueYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease, Liability, Payments, Due Year Four</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilityPaymentsDueYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2030</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IntangibleAssetsNetExcludingGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Intangible Assets, Net (Excluding Goodwill), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IntangibleAssetsNetExcludingGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Intangible Assets, Net (Excluding Goodwill)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IntangibleAssetsNetExcludingGoodwill_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Intangible assets, net of accumulated amortization of 159,511 and 157,437</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lease liability.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Present value of lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeasePayments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeasePayments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Assets:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_CommitmentsAndContingenciesLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments and Contingencies [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_CommitmentsAndContingenciesLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Commitments and contingencies.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Prepaid expenses and other current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Prepaid Expense and Other Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AmortizationOfFinancingCostsAndDiscounts_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Amortization of Debt Issuance Costs and Discounts, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AmortizationOfFinancingCostsAndDiscounts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amortization of Debt Issuance Costs and Discounts</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AmortizationOfFinancingCostsAndDiscounts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amortization of debt discount and debt issuance costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ReceivableTaxDeferralsTaxCreditsAndEmployeeWageSupportReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Due from government assistance programs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ReceivableTaxDeferralsTaxCreditsAndEmployeeWageSupportReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Receivable Tax Deferrals Tax Credits And Employee Wage Support Receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ReceivableTaxDeferralsTaxCreditsAndEmployeeWageSupportReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Receivable Tax Deferrals Tax Credits And Employee Wage Support Receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalYearFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Fiscal Year Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_DerivativeCapInterestRateDescription_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Cap Interest Rate Description</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_DerivativeCapInterestRateDescription_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Derivative cap interest rate description.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_DerivativeCapInterestRateDescription_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivative, cap interest rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Accumulated Other Comprehensive Income (Loss) [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Changes in Accumulated Other Comprehensive (Loss) Income, Net of Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Assets [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Investing activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Payable, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Accounts Payable, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpenseNonoperating_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Interest Expense, Nonoperating, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpenseNonoperating_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Expense, Nonoperating</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpenseNonoperating_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillImpairmentLossStatementOfIncomeOrComprehensiveIncomeExtensibleEnumeration_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill, Impairment Loss, Statement of Income or Comprehensive Income [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeMaturityDates_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivative, date of maturity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeMaturityDates_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative, Contract End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lease, liability, noncurrent.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease, Liability, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Other Liabilities, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Due to unconsolidated related parties</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLeaseNotYetCommencedTermOfContract1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Lease Not yet Commenced, Term of Contract</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLeaseNotYetCommencedTermOfContract1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease not yet commenced term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueDisclosuresAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Disclosures [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments and Contingencies Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Year One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2027</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Long-Term Line of Credit, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Line of Credit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Line of credit. outstanding borrowings</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Letters of Credit Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeInstrumentRiskAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Instrument [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unrecognized stock-based compensation expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Amount, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_DebtInstrumentRevolvingLoansOutstandingMaximumPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Debt instrument revolving loans outstanding maximum percentage.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_DebtInstrumentRevolvingLoansOutstandingMaximumPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument Revolving Loans Outstanding Maximum Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_DebtInstrumentRevolvingLoansOutstandingMaximumPercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt instrument revolving loans outstanding maximum percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsidiarySaleOfStockAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ReimbursementsOffsettingCostOfServices_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Reimbursements Offsetting Cost Of Services</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ReimbursementsOffsettingCostOfServices_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Reimbursements offsetting cost of services.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ReimbursementsOffsettingCostOfServices_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Reimbursements offsetting cost of services</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_DeferredOfferingCostsIncludedInAccountsPayableAndAccruedLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Deferred offering costs included in accounts payable and accrued liabilities.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_DeferredOfferingCostsIncludedInAccountsPayableAndAccruedLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Offering Costs Included in Accounts Payable and Accrued Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_DeferredOfferingCostsIncludedInAccountsPayableAndAccruedLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred offering costs included in accounts payable and accrued liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ProfitInterestUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Profit interest units.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ProfitInterestUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Profit Interest Units [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ProfitInterestUnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">PIU</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ReimbursementOfCenterOperatingExpensesOffsettingCostOfServices_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Reimbursement of center operating expenses offsetting cost of services.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ReimbursementOfCenterOperatingExpensesOffsettingCostOfServices_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Reimbursement Of Center Operating Expenses Offsetting Cost Of Services</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ReimbursementOfCenterOperatingExpensesOffsettingCostOfServices_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Reimbursement of center operating expenses offsetting cost of services</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Cash used in investing activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Weighted Average Remaining Lease Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseWeightedAverageRemainingLeaseTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted average remaining lease term (in years) (Finance)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_Security12bTitle_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Title of 12(b) Security</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ProceedsFromDeferredCompensationAssetTrustRedemptions_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Proceeds from deferred compensation asset trust redemptions.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ProceedsFromDeferredCompensationAssetTrustRedemptions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds From Deferred Compensation Asset Trust Redemptions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ProceedsFromDeferredCompensationAssetTrustRedemptions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from deferred compensation asset trust redemptions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueConversionOfUnits_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Value, Conversion of Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueConversionOfUnits_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Effect of remeasured at fair value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Instruments and Hedging Activities Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Risk Management and Derivatives</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MoneyMarketFundsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Money Market Funds [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MoneyMarketFundsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Money Market Funds</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related and Nonrelated Parties [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income Taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Remainder of Fiscal Year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Remainder of 2026</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherLiabilitiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Liabilities, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherLiabilitiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other long-term liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilitiesPaymentsDueAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lease liabilities, payments due.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilitiesPaymentsDueAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease Liabilities, Payments Due [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilitiesPaymentsDueAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total Leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Finance Lease, Right-of-Use Asset, after Accumulated Amortization, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Right-of-Use Asset, after Accumulated Amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Finance lease right-of-use assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_OperatingAndFinanceLeaseLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total current lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_OperatingAndFinanceLeaseLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Operating and finance lease liabilities current.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_OperatingAndFinanceLeaseLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating And Finance Lease Liabilities Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity, Increase (Decrease) in Operating Capital [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Changes in assets and liabilities, net of effects of acquisitions:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LettersOfCreditOutstandingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Letters of Credit Outstanding, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LettersOfCreditOutstandingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Letters of credit outstanding, amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Recurring and Nonrecurring [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Acquisitions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefits_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Unrecognized Tax Benefits, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefits_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Unrecognized Tax Benefits, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefits_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Unrecognized Tax Benefits</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefits_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Receivable related to uncertain tax positions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Additional Paid-in Capital [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Additional Paid-in Capital</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementLocationAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Income Location, Balance [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_TradingSymbol_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Trading Symbol</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ClassB3UnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Class B3 Units.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ClassB3UnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class B3 Units [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ClassB3UnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Class B-3 Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transaction [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event Type [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued compensation and related expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Employee-related Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Employee-related Liabilities, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Financing activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unused letters of credit fee interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Line of Credit Facility, Unused Capacity, Commitment Fee Percentage</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Payable and Accrued Liabilities Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableAndAccruedLiabilitiesDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts Payable and Accrued Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ScheduleOfMaturityOfOperatingAndFinanceLeaseLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Schedule of maturity of operating and finance lease liabilities.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ScheduleOfMaturityOfOperatingAndFinanceLeaseLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule Of Maturity Of Operating And Finance Lease Liabilities [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ScheduleOfMaturityOfOperatingAndFinanceLeaseLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Maturity of Lease Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total lease payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, Undiscounted Excess Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Less imputed interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Less imputed interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ScheduleOfOtherDeferredCompensationPlansDisclosuresTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Other Deferred Compensation Plans Disclosures [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ScheduleOfOtherDeferredCompensationPlansDisclosuresTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Schedule of other deferred compensation plans disclosures.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ScheduleOfOtherDeferredCompensationPlansDisclosuresTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Composition of Underlying Investments in Deferred Compensation Plan Trust Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_EarningsPerShareBasicsAndDilutedAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Earnings Per Share Basics And Diluted Abstract.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_EarningsPerShareBasicsAndDilutedAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share Basics And Diluted Abstract</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_EarningsPerShareBasicsAndDilutedAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net (loss) income per common share:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementEquityComponentsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity Components [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_CashPaidForAmountsIncludedInTheMeasurementOfOperatingLeaseLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Cash paid for amounts included in the measurement of operating lease liabilities.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_CashPaidForAmountsIncludedInTheMeasurementOfOperatingLeaseLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Paid For Amounts Included In The Measurement Of Operating Lease Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_CashPaidForAmountsIncludedInTheMeasurementOfOperatingLeaseLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash paid for amounts included in the measurement of operating lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeAssetNoncurrentStatementOfFinancialPositionExtensibleEnumeration_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Asset, Noncurrent, Statement of Financial Position [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_DerivativeInceptionMonthAndYear_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Inception Month And Year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_DerivativeInceptionMonthAndYear_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Derivative inception month and year.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_DerivativeInceptionMonthAndYear_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivative inception month and year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InsuranceSettlementsReceivableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Insurance Settlements Receivable, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InsuranceSettlementsReceivableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Insurance receivables</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquityComponentDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity Component [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_DerivativeCommencementMonthAndYear_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Commencement Month And Year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_DerivativeCommencementMonthAndYear_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Derivative commencement month and year.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_DerivativeCommencementMonthAndYear_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivative commencement month and year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill and Intangible Assets Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestIncomeInterestEarningAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Income, Interest-Earning Asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestIncomeInterestEarningAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Interest Income, Interest-Earning Asset, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestIncomeInterestEarningAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestIncomeInterestEarningAsset_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Interest income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IPOMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">IPO [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IPOMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">IPO</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_EquityBasedCompensationExpenseIncomeTaxBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income tax benefit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_EquityBasedCompensationExpenseIncomeTaxBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Equity-based compensation expense income tax benefit.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_EquityBasedCompensationExpenseIncomeTaxBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity-Based Compensation Expense Income Tax Benefit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Exercise terms</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Expiration Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ExtendedCommitmentsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Extended Commitments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ExtendedCommitmentsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Extended Commitments [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ExtendedCommitmentsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Extended commitments.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MaximumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Maximum [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MaximumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Maximum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_TwoThousandTwentyFiveAcquisitionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand Twenty Five Acquisitions [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_TwoThousandTwentyFiveAcquisitionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two Thousand Twenty Five Acquisitions [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_TwoThousandTwentyFiveAcquisitionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2025 Acquisitions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_NumberOfSitesOfferedForEducationalServices_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Number of sites offered for educational services.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_NumberOfSitesOfferedForEducationalServices_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number of Sites Offered for Educational Services</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_NumberOfSitesOfferedForEducationalServices_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of sites offered for educational services</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statistical Measurement [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ScheduleOfImpairmentExpenseOfGoodwillAndLong-LivedAssetsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Impairment Expense of Goodwill and Long-Lived Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ScheduleOfImpairmentExpenseOfGoodwillAndLong-LivedAssetsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Impairment Expense of Goodwill and Long-lived Assets [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ScheduleOfImpairmentExpenseOfGoodwillAndLong-LivedAssetsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Schedule of impairment expense of goodwill and long-lived assets.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finite-Lived Intangible Assets, Accumulated Amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated amortization, intangible assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Value, Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, par value $0.01; 750,000 shares authorized; 118,428 shares issued and outstanding as of April 4, 2026 and 118,340 shares issued and outstanding as of January 3, 2026</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeFixedInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative, Fixed Interest Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeFixedInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivative, fixed interest rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeasePrincipalPayments_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Payments of financing lease obligations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeasePrincipalPayments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Principal Payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_FirstLienRevolvingCreditFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">First lien revolving credit facility.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_FirstLienRevolvingCreditFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">First Lien Revolving Credit Facility [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_FirstLienRevolvingCreditFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">First Lien Revolving Credit Facility</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Asset, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest rate derivative contracts</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Interest rate derivative contracts, assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DistributionMadeToLimitedPartnerCashDistributionsPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Distribution Made to Limited Partner, Cash Distributions Paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DistributionMadeToLimitedPartnerCashDistributionsPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Distribution made to limited partner, cash distributions paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Reclassification out of Accumulated Other Comprehensive Income [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ReclassificationOutOfAccumulatedOtherComprehensiveIncomeTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Amounts Affecting Unaudited Condensed Consolidated Statements of Operations and Comprehensive (Loss) Income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_TwoForwardStartingPay-Fixed-Receive-FloatInterestRateSwapContractsTwoMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Forward Starting Pay-Fixed-Receive-Float Interest Rate Swap Contracts Two [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_TwoForwardStartingPay-Fixed-Receive-FloatInterestRateSwapContractsTwoMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two forward starting pay-fixed-receive-float interest rate swap contracts two.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_TwoForwardStartingPay-Fixed-Receive-FloatInterestRateSwapContractsTwoMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Two Forward Starting Pay-Fixed-Receive-Float Interest Rate Swap Contracts Two</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_DeferredCloudComputingImplementationCostsIncludedInAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Cloud Computing Implementation Costs Included In Accounts Payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_DeferredCloudComputingImplementationCostsIncludedInAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Deferred cloud computing implementation costs included in accounts payable.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_DeferredCloudComputingImplementationCostsIncludedInAccountsPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred cloud computing implementation costs included in accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AmortizationOfFinancingCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amortization of Debt Issuance Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AmortizationOfFinancingCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amortization of debt issuance costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Shares Authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred stock, shares authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Payable, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostsAndExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total costs and expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostsAndExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Costs and Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LessorOperatingLeaseTermOfContract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LessorOperatingLeaseTermOfContract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessor, Operating Lease, Term of Contract</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDebtTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Debt [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDebtTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Long-Term Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ReimbursementOfCostOfServices_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Reimbursement Of Cost Of Services.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ReimbursementOfCostOfServices_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Reimbursement Of Cost Of Services</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ReimbursementOfCostOfServices_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Reimbursement of cost of services</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transaction [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueFromContractWithCustomerTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revenue from Contract with Customer [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueFromContractWithCustomerTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Revenue Recognition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityRegistrantName_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Registrant Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityRegistrantName_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Registrant Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAcceleratedCompensationCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Accelerated Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAcceleratedCompensationCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Allocation of share based compensation accelerated costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNonoperatingIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Other Nonoperating Income (Expense), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNonoperatingIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Nonoperating Income (Expense)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNonoperatingIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Other income, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accumulated Other Comprehensive Income (Loss) [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GovernmentAssistanceTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Government Assistance, Type [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Events [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableAndAccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Payable and Accrued Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableAndAccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total accounts payable and accrued liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableAndAccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Accounts payable and accrued liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableAndAccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total accounts payable and accrued liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_PayFixedReceiveFloatInterestRateSwapContractMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Pay-Fixed-Receive-Float Interest Rate Swap Contract [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_PayFixedReceiveFloatInterestRateSwapContractMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Pay-Fixed-Receive-Float Interest Rate Swap Contract [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_PayFixedReceiveFloatInterestRateSwapContractMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Pay-Fixed-Receive-Float Interest Rate Swap Contract</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeVariableInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative, Variable Interest Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeVariableInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivative variable rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Income Tax Expense (Benefit), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Expense (Benefit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income tax benefit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Income tax expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Income tax effect</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Income tax (benefit) expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_BoardMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Board</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_BoardMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Board [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_BoardMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Board.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_RightOfUseAssetsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Right-of-use assets.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_RightOfUseAssetsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Right-of-Use Assets [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_RightOfUseAssetsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Assets:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostsAndExpensesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Costs and Expenses [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostsAndExpensesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Costs and expenses:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Thereafter</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lessee operating lease liability payments due after year four.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee Operating Lease Liability Payments Due After Year Four</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Common Stock, Shares Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Accumulated Other Comprehensive Income (Loss), Net of Tax, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accumulated Other Comprehensive Income (Loss), Net of Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated other comprehensive loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_DeferredEmployeeRetentionCreditsNonCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Employee Retention Credits Non Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_DeferredEmployeeRetentionCreditsNonCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Deferred employee retention credits non current.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_DeferredEmployeeRetentionCreditsNonCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred employee retention credits noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Payments to Acquire Property, Plant, and Equipment, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments to Acquire Property, Plant, and Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Purchases of property and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnInvestments_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Gain (Loss) on Investments, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnInvestments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gain (Loss) on Investments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnInvestments_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Realized and unrealized losses from investments held in deferred compensation asset trusts</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Assets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Assets_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LesseeOperatingAndFinanceLeasesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lessee operating and finance leases.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LesseeOperatingAndFinanceLeasesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee Operating and Finance Leases [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LesseeOperatingAndFinanceLeasesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Statement [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_Share-BasedPaymentArrangementRemainingTwelveTranchesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Remaining Twelve Tranches [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_Share-BasedPaymentArrangementRemainingTwelveTranchesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share-based payment arrangement, remaining twelve tranches.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_Share-BasedPaymentArrangementRemainingTwelveTranchesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Equal Quarterly Installments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestRateCapMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Rate Cap [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestRateCapMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest Rate Cap</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilitiesNonCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Liabilities-long-term:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilitiesNonCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lease liabilities Non-current.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_LeaseLiabilitiesNonCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease Liabilities Non-current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ReimbursementOfCashTaxRefunds_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Reimbursement Of Cash Tax Refunds</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ReimbursementOfCashTaxRefunds_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Reimbursement Of Cash Tax Refunds.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ReimbursementOfCashTaxRefunds_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Reimbursements of cash tax refunds</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Selling, General and Administrative Expenses [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpensesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Selling, General and Administrative Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_IncrementalFirstLienTermLoanFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Incremental First Lien Term Loan Facility</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_IncrementalFirstLienTermLoanFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Incremental first lien term loan facility.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_IncrementalFirstLienTermLoanFacilityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Incremental First Lien Term Loan Facility [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseCostAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease, Cost [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseCostAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Lease expense:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Earnings Per Share, Diluted, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share, Diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SelfInsuranceReserveCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Self Insurance Reserve, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SelfInsuranceReserveCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Self-insurance obligations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ClassB1UnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Class B-1 Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ClassB1UnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Class B1 Units.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ClassB1UnitsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class B1 Units [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_TitleOfIndividualWithRelationshipToEntityDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Title and Position [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_InitialPublicOfferingPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Initial Public Offering</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_InitialPublicOfferingPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Initial Public Offering Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_InitialPublicOfferingPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Initial Public Offering Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CityAreaCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">City Area Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationConsiderationTransferredLiabilitiesIncurred_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination, Consideration Transferred, Liabilities Incurred</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessCombinationConsiderationTransferredLiabilitiesIncurred_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Business acquisition, holdbacks</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_TwoThousandTwentyThreeAcquisitionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2023 Acquisitions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_TwoThousandTwentyThreeAcquisitionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two thousand twenty three acquisitions.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_TwoThousandTwentyThreeAcquisitionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand Twenty Three Acquisitions [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Net of Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other comprehensive income (loss), net of tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Total effect on other comprehensive income, net of tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total Effect on Other Comprehensive (Loss) Income, net of tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_GovernmentSupportDeferredLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Government support, deferred liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_GovernmentSupportDeferredLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Government Support Deferred Liability.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_GovernmentSupportDeferredLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Government Support Deferred Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Finance lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Liability, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Long-term lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Line of Credit Facility, Maximum Borrowing Capacity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Letters of credit maximum borrowing capacity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ContingentConsiderationRangeOfUndiscountedAmountPayableUnderAssetPurchaseAgreement_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Contingent Consideration Range of Undiscounted Amount Payable Under Asset Purchase Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ContingentConsiderationRangeOfUndiscountedAmountPayableUnderAssetPurchaseAgreement_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Contingent consideration range of undiscounted amount payable under asset purchase agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_ContingentConsiderationRangeOfUndiscountedAmountPayableUnderAssetPurchaseAgreement_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Contingent consideration range of undiscounted amount payable under asset purchase agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessAcquisitionLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Combination [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Cash Flow Hedge, Gain (Loss), Reclassification, after Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossReclassificationAfterTax_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Reclassifications to net (loss) income of previously deferred gains</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VariableLeaseCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Variable lease expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_VariableLeaseCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Variable Lease, Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_LitigationCaseAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Litigation Case [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Weighted Average Remaining Lease Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted average remaining lease term (in years) (Operating)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityNoteStockSplitConversionRatio1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, convertible ratio</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityNoteStockSplitConversionRatio1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stockholders' Equity Note, Stock Split, Conversion Ratio</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Shares, Restricted Stock Award, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock upon settlement of restricted stock units, shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease, Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseCost_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total lease expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_TwoForwardStartingPay-Fixed-Receive-FloatInterestRateSwapContractsOneMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Two Forward Starting Pay-Fixed-Receive-Float Interest Rate Swap Contracts One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_TwoForwardStartingPay-Fixed-Receive-FloatInterestRateSwapContractsOneMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Forward Starting Pay-fixed-receive-float Interest Rate Swap Contracts One [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_TwoForwardStartingPay-Fixed-Receive-FloatInterestRateSwapContractsOneMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two Forward Starting Pay-fixed-receive-float Interest Rate Swap Contracts One [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LetterOfCreditMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Letter of Credit [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LetterOfCreditMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Letter of Credit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Liability, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest rate derivative contracts, current liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Property, Plant and Equipment, Net, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Fixed assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property and equipment, net of accumulated depreciation of 589,254 and 582,808</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_OperatingAndFinanceLeaseLiabilitiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total long-term lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_OperatingAndFinanceLeaseLiabilitiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Operating and finance lease liabilities noncurrent.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_OperatingAndFinanceLeaseLiabilitiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating And Finance Lease Liabilities Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Finance lease right-of-use assets obtained in exchange for finance lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Right-of-Use Asset Obtained in Exchange for Finance Lease Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Income (Loss)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">(Loss) income from operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_CommitmentsAndContingenciesTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments and Contingencies [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_CommitmentsAndContingenciesTable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Commitments and contingencies.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Retained Earnings [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Retained Earnings (Deficit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Share-Based Payment Arrangement, Noncash Expense, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Noncash Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock-based compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensation_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Stock-based compensation expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfStockIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments of Stock Issuance Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfStockIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Underwriting discounts and commissions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfStockIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Payments of deferred offering costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Operating lease not yet commenced</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Unrecorded Unconditional Purchase Obligation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unrecorded Unconditional Purchase Obligation, Including Lease Not yet Commenced, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecordedUnconditionalPurchaseObligationBalanceSheetAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Unrecorded Unconditional Purchase Obligation, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Weighted Average Discount Rate, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted average discount rate (Operating)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease liabilities-long-term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Operating lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-term lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel1Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Inputs, Level 1 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel1Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Quoted Price in Active Markets for Identical Assets (Level 1)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Cash used in financing activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseCostTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease, Cost [Table Text Block]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ManagementFeePayable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Management Fee Payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ManagementFeePayable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Management Fee</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxLiabilitiesNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Income Tax Liabilities, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxLiabilitiesNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred income taxes, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Investments, Fair Value Disclosure, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investments, Fair Value Disclosure</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Investments, fair value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeLiabilitiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest rate derivative contracts, liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeLiabilitiesNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Liability, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeContractTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Contract [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_TwoForwardStartingPay-Fixed-Receive-FloatInterestRateSwapContractsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Forward Starting Pay-fixed-receive-float Interest Rate Swap Contracts [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_TwoForwardStartingPay-Fixed-Receive-FloatInterestRateSwapContractsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two forward starting pay-fixed-receive-float interest rate swap contracts.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_TwoForwardStartingPay-Fixed-Receive-FloatInterestRateSwapContractsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Two Forward Starting Pay-Fixed-Receive-Float Interest Rate Swap Contracts</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfGoodwillTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Goodwill [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_FirstLienRevolvingCreditFacilityAmendmentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">First Lien Revolving Credit Facility Amendment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_FirstLienRevolvingCreditFacilityAmendmentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">First lien revolving credit facility amendment.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_FirstLienRevolvingCreditFacilityAmendmentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">First Lien Revolving Credit Facility Amendment [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityInteractiveDataCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Interactive Data Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementLocationDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Income Location, Balance [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostsAndExpensesRelatedParty_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Costs and Expenses, Related Party</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_LocalPhoneNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Local Phone Number</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="klc_EmployeeRetentionCreditMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Employee Retention Credit Member.</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherCurrentLiabilitiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other Current Liabilities</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Revenue</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Revenue</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeLiabilityCurrentStatementOfFinancialPositionExtensibleEnumeration_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Liability, Current, Statement of Financial Position [Extensible Enumeration]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2030</link:label>
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  <xsd:element id="klc_ClassB1UnitsMember" name="ClassB1UnitsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="klc_AdjustedBalanceOfGoodwillAmount" name="AdjustedBalanceOfGoodwillAmount" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="klc_LeaseLiabilityPaymentsDueYearThree" name="LeaseLiabilityPaymentsDueYearThree" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="klc_TwoPayFixedReceiveFloatInterestRateSwapContractMember" name="TwoPayFixedReceiveFloatInterestRateSwapContractMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="klc_TwoThousandTwentyFourAcquisitionsMember" name="TwoThousandTwentyFourAcquisitionsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="klc_LesseeOperatingLeaseLeaseExpectedCommencedTerm" name="LesseeOperatingLeaseLeaseExpectedCommencedTerm" type="xbrli:gYearItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="klc_FirstLienTermLoanFacilityMember" name="FirstLienTermLoanFacilityMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="klc_TwoThousandAndTwentyTwoIncentiveAwardPlanMember" name="TwoThousandAndTwentyTwoIncentiveAwardPlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="klc_EarlyChildhoodEducationCentersMember" name="EarlyChildhoodEducationCentersMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="klc_FirstLienRevolvingCreditFacilityAmendmentMember" name="FirstLienRevolvingCreditFacilityAmendmentMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="klc_TwoThousandAndTwentyTwoStockOptionPlanMember" name="TwoThousandAndTwentyTwoStockOptionPlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="klc_LeaseLiabilitiesCurrentAbstract" name="LeaseLiabilitiesCurrentAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="klc_NumberOfCommunityBasedAndEmployerSponsoredEarlyChildhoodEducationAndCareServicesCenters" name="NumberOfCommunityBasedAndEmployerSponsoredEarlyChildhoodEducationAndCareServicesCenters" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="klc_OperatingAndFinanceLeaseLiabilitiesCurrent" name="OperatingAndFinanceLeaseLiabilitiesCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="klc_TaxPaymentsRelatedToNetSettlementOfRestrictedStockUnits" name="TaxPaymentsRelatedToNetSettlementOfRestrictedStockUnits" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="klc_IndependentBoardMembersMember" name="IndependentBoardMembersMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="klc_LeaseLiabilityPaymentsDueYearFour" name="LeaseLiabilityPaymentsDueYearFour" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="klc_NumberOfLeasedCenterSitesImpactedByLeaseAmendment" name="NumberOfLeasedCenterSitesImpactedByLeaseAmendment" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="klc_LeaseLiabilityPaymentsDueAfterYearFour" name="LeaseLiabilityPaymentsDueAfterYearFour" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="klc_ReimbursementOfFoodCost" name="ReimbursementOfFoodCost" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="klc_EmployeeRetentionCreditsReceivableCurrent" name="EmployeeRetentionCreditsReceivableCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="klc_BeforeAndAfterSchoolSitesMember" name="BeforeAndAfterSchoolSitesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="klc_PrincipalPaymentsOfLongTermDebt" name="PrincipalPaymentsOfLongTermDebt" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="klc_DeferredOfferingCostsIncludedInAccountsPayableAndAccruedLiabilities" name="DeferredOfferingCostsIncludedInAccountsPayableAndAccruedLiabilities" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="klc_RelatedPartyTransactionRelatedPartiesRent" name="RelatedPartyTransactionRelatedPartiesRent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="klc_DerivativeCommencementDate" name="DerivativeCommencementDate" type="xbrli:dateItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="klc_ReimbursementOfCashTaxRefunds" name="ReimbursementOfCashTaxRefunds" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="klc_LeaseLiabilitiesNonCurrentAbstract" name="LeaseLiabilitiesNonCurrentAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="klc_NonCashOperatingActivitiesAbstract" name="NonCashOperatingActivitiesAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="klc_NumberOfSitesOfferedForEducationalServices" name="NumberOfSitesOfferedForEducationalServices" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="klc_CashPaidForAmountsIncludedInTheMeasurementOfOperatingLeaseLiabilities" name="CashPaidForAmountsIncludedInTheMeasurementOfOperatingLeaseLiabilities" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="klc_ReimbursementOfCostOfServices" name="ReimbursementOfCostOfServices" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="klc_NumberOfChildrenWithLicenseCapacity" name="NumberOfChildrenWithLicenseCapacity" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="klc_EarningsPerShareBasicsAndDilutedAbstract" name="EarningsPerShareBasicsAndDilutedAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="klc_NonExtendedCommitmentsMember" name="NonExtendedCommitmentsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="klc_ProfitInterestUnitsMember" name="ProfitInterestUnitsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="klc_CreditFacility" name="CreditFacility" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="klc_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFour" name="LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFour" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="klc_EmployeeRetentionCreditMember" name="EmployeeRetentionCreditMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="klc_PayFixedReceiveFloatInterestRateSwapContractMember" name="PayFixedReceiveFloatInterestRateSwapContractMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="klc_AdjustmentsToAdditionalPaidInCapitalDistributionToKcParent" name="AdjustmentsToAdditionalPaidInCapitalDistributionToKcParent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="klc_CommitmentsAndContingenciesLineItems" name="CommitmentsAndContingenciesLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="klc_LeaseLiability" name="LeaseLiability" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="klc_OperatingAndFinanceLeaseRightOfUseAsset" name="OperatingAndFinanceLeaseRightOfUseAsset" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="klc_LeaseLiabilityPaymentsDue" name="LeaseLiabilityPaymentsDue" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="klc_CommitmentsAndContingenciesTable" name="CommitmentsAndContingenciesTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="klc_LesseeOperatingAndFinanceLeasesTextBlock" name="LesseeOperatingAndFinanceLeasesTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="klc_TwoThousandTwentySixAcquisitionsMember" name="TwoThousandTwentySixAcquisitionsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="klc_FirstLienRevolvingCreditFacilityMember" name="FirstLienRevolvingCreditFacilityMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="klc_DerivativeVariableRateDescription" name="DerivativeVariableRateDescription" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="klc_LineOfCreditFacilityFrontingFeePercentage" name="LineOfCreditFacilityFrontingFeePercentage" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="klc_LeaseLiabilitiesPaymentsDueAbstract" name="LeaseLiabilitiesPaymentsDueAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="klc_CommonStockConvertibleConversionRatio" name="CommonStockConvertibleConversionRatio" type="xbrli:pureItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="klc_EmployeeRetentionCreditsReceivable" name="EmployeeRetentionCreditsReceivable" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="klc_InitialPublicOfferingPolicyPolicyTextBlock" name="InitialPublicOfferingPolicyPolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="klc_ScheduleOfOtherDeferredCompensationPlansDisclosuresTableTextBlock" name="ScheduleOfOtherDeferredCompensationPlansDisclosuresTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="klc_ExtendedAndNonExtendedCommitmentsMember" name="ExtendedAndNonExtendedCommitmentsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="klc_DeferredEmployeeRetentionCreditsNonCurrent" name="DeferredEmployeeRetentionCreditsNonCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="klc_OperatingAndFinanceLeaseLiabilities" name="OperatingAndFinanceLeaseLiabilities" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="klc_ProfitInterestUnitsPlanMember" name="ProfitInterestUnitsPlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="klc_EquityBasedCompensationExpenseIncomeTaxBenefit" name="EquityBasedCompensationExpenseIncomeTaxBenefit" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="klc_RelatedPartyTransactionPartnersGroupManagementServices" name="RelatedPartyTransactionPartnersGroupManagementServices" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="klc_TwoThousandTwentyThreeAcquisitionsMember" name="TwoThousandTwentyThreeAcquisitionsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="klc_OtherCreditFacilityMember" name="OtherCreditFacilityMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="klc_CivilActionSettlementAgreementMember" name="CivilActionSettlementAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="klc_ContingentConsiderationRangeOfUndiscountedAmountPayableUnderAssetPurchaseAgreement" name="ContingentConsiderationRangeOfUndiscountedAmountPayableUnderAssetPurchaseAgreement" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="klc_ProceedsFromDeferredCompensationAssetTrustRedemptions" name="ProceedsFromDeferredCompensationAssetTrustRedemptions" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="klc_ReimbursementsOffsettingCostOfServices" name="ReimbursementsOffsettingCostOfServices" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="klc_ScheduleOfMaturityOfOperatingAndFinanceLeaseLiabilitiesTableTextBlock" name="ScheduleOfMaturityOfOperatingAndFinanceLeaseLiabilitiesTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="klc_Rule10B51ArrangementModifiedFlag" name="Rule10B51ArrangementModifiedFlag" type="xbrli:booleanItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="klc_SeniorSecuredCreditFacilitiesMember" name="SeniorSecuredCreditFacilitiesMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="klc_RightOfUseAssetsAbstract" name="RightOfUseAssetsAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="klc_ImpairmentLosses" name="ImpairmentLosses" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="klc_LeaseLiabilityPaymentsDueRemainderOfFiscalYear" name="LeaseLiabilityPaymentsDueRemainderOfFiscalYear" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="klc_LeaseAgreementMember" name="LeaseAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
</xsd:schema>
