Derivative cap interest rate description.

No definition available.

Name:	klc_DerivativeCapInterestRateDescription
Namespace Prefix:	klc_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Derivative commencement date.

+ References

No definition available.

+ Details

Name:	klc_DerivativeCommencementDate
Namespace Prefix:	klc_
Data Type:	xbrli:dateItemType
Balance Type:	na
Period Type:	duration

- Definition

Derivative inception month and year.

+ References

No definition available.

+ Details

Name:	klc_DerivativeInceptionMonthAndYear
Namespace Prefix:	klc_
Data Type:	xbrli:gYearMonthItemType
Balance Type:	na
Period Type:	duration

- Definition

Fixed interest rate related to the interest rate derivative.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 815
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 5
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480434/815-10-50-5

+ Details

Name:	us-gaap_DerivativeFixedInterestRate
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 815
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 5A
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480434/815-10-50-5A

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 505
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 18
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481112/505-10-50-18

Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 815
-SubTopic 20
-Name Accounting Standards Codification
-Section 25
-Paragraph 6A
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480682/815-20-25-6A

+ Details

Name:	us-gaap_DerivativeLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Date derivative contract ends, in YYYY-MM-DD format.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 210
-Name Accounting Standards Codification
-Section 50
-Paragraph 6
-Subparagraph (e)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478795/946-210-50-6

Reference 2: http://www.xbrl.org/2003/role/exampleRef
-Topic 946
-SubTopic 210
-Name Accounting Standards Codification
-Section 55
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477439/946-210-55-1

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 210
-Name Accounting Standards Codification
-Section 50
-Paragraph 6
-Subparagraph (f)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478795/946-210-50-6

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 320
-Name Accounting Standards Codification
-Section S99
-Paragraph 5
-Subparagraph (SX 210.12-13(Column A)(Footnote 3))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477271/946-320-S99-5

Reference 5: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 320
-Name Accounting Standards Codification
-Section S99
-Paragraph 5C
-Subparagraph (SX 210.12-13C(Column D))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477271/946-320-S99-5C

Reference 6: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 320
-Name Accounting Standards Codification
-Section S99
-Paragraph 5
-Subparagraph (SX 210.12-13(Column F))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477271/946-320-S99-5

Reference 7: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 320
-Name Accounting Standards Codification
-Section S99
-Paragraph 5A
-Subparagraph (SX 210.12-13A(Column C))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477271/946-320-S99-5A

Reference 8: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 320
-Name Accounting Standards Codification
-Section S99
-Paragraph 5B
-Subparagraph (SX 210.12-13B(Column D))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477271/946-320-S99-5B

+ Details

Name:	us-gaap_DerivativeMaturityDates
Namespace Prefix:	us-gaap_
Data Type:	xbrli:dateItemType
Balance Type:	na
Period Type:	duration

- Definition

Nominal or face amount used to calculate payment on derivative.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 815
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1A
-Subparagraph (d)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480434/815-10-50-1A

Reference 2: http://www.xbrl.org/2003/role/exampleRef
-Topic 815
-SubTopic 10
-Name Accounting Standards Codification
-Section 55
-Paragraph 181
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480401/815-10-55-181

Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 815
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1B
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480434/815-10-50-1B

+ Details

Name:	us-gaap_DerivativeNotionalAmount
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	na
Period Type:	instant

- Definition

Variable interest rate in effect as of the balance sheet date related to the interest rate derivative.

+ References

+ Details

Name:	us-gaap_DerivativeVariableInterestRate
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

The estimated net amount of unrealized gains or losses on interest rate cash flow hedges as of the balance sheet date expected to be reclassified to earnings within the next twelve months.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 815
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480870/815-30-50-1

+ Details

Name:	us-gaap_InterestRateCashFlowHedgeGainLossToBeReclassifiedDuringNext12MonthsNet
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Details

Name:	srt_RangeAxis=srt_MinimumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_StatementScenarioAxis=srt_ScenarioForecastMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DerivativeInstrumentRiskAxis=us-gaap_InterestRateSwapMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DerivativeInstrumentRiskAxis=klc_PayFixedReceiveFloatInterestRateSwapContractMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DerivativeInstrumentRiskAxis=klc_TwoPayFixedReceiveFloatInterestRateSwapContractMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DerivativeInstrumentRiskAxis=klc_TwoForwardStartingPay-Fixed-Receive-FloatInterestRateSwapContractsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DerivativeInstrumentRiskAxis=klc_TwoForwardStartingPay-Fixed-Receive-FloatInterestRateSwapContractsOneMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DerivativeInstrumentRiskAxis=klc_TwoForwardStartingPay-Fixed-Receive-FloatInterestRateSwapContractsTwoMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Risk Management and Derivatives - Additional Information (Details) - USD ($) $ in Millions			6 Months Ended	24 Months Ended
	Dec. 31, 2027	Dec. 31, 2026	Jul. 04, 2026	Jul. 04, 2026	Mar. 31, 2025	Feb. 29, 2024	Jan. 31, 2024
Derivative [Line Items]
Derivative, cap interest rate			greater of three-month SOFR or 0.50%
Minimum
Derivative [Line Items]
Derivative variable rate			0.50%	0.50%
Scenario Forecast \| Minimum
Derivative [Line Items]
Derivative variable rate		0.50%
Interest Rate Swap
Derivative [Line Items]
Derivative, commencement date				Jun. 28, 2024
Derivative, date of maturity				Dec. 31, 2026
Deferred gains recognized within accumulated other comprehensive loss reclassified as decrease in interest expense within the next twelve months			$ 0.5	$ 0.5
Pay-Fixed-Receive-Float Interest Rate Swap Contract
Derivative [Line Items]
Notional amount of derivative instrument							$ 400.0
Derivative, fixed interest rate							3.85%
Two Pay-Fixed-Receive-Float Interest Rate Swap Contract
Derivative [Line Items]
Notional amount of derivative instrument						$ 400.0
Derivative, fixed interest rate						3.89%
Two Forward Starting Pay-Fixed-Receive-Float Interest Rate Swap Contracts
Derivative [Line Items]
Derivative, cap interest rate		greater of three-month SOFR or 0.50%
Notional amount of derivative instrument					$ 500.0
Derivative, commencement date		Dec. 31, 2026
Derivative inception month and year			2025-03
Derivative, date of maturity	Dec. 31, 2027
Two Forward Starting Pay-Fixed-Receive-Float Interest Rate Swap Contracts One
Derivative [Line Items]
Derivative, fixed interest rate					3.72%
Two Forward Starting Pay-Fixed-Receive-Float Interest Rate Swap Contracts Two
Derivative [Line Items]
Derivative, fixed interest rate					3.74%