Related Party Transactions, Expense Support and Conditional Reimbursement Agreement (Details) - Advisor [Member] - USD ($)	3 Months Ended
Mar. 31, 2023	Dec. 31, 2022
Expense Support and Conditional Reimbursement Agreement [Abstract]
Percentage of other operating expenses for applicable quarter-end net asset value	1.00%
Reimbursement payment obligation	$ 0	$ 0
Future potential reimbursement amount	625,598
Additional expense support	$ 0
Maximum [Member]
Expense Support and Conditional Reimbursement Agreement [Abstract]
Reimbursement period of expense payments	3 years
Reimbursement payment period	45 days

No definition available.

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Namespace Prefix:	klcc_
Data Type:	xbrli:stringItemType
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- Definition

The amount incurred from formation that is subject to future potential reimbursement.

+ References

No definition available.

+ Details

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Namespace Prefix:	klcc_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Percentage of other operating expenses of the company's applicable quarter-end net asset value on an annualized basis.

+ References

No definition available.

+ Details

Name:	klcc_PercentageOfOtherOperatingExpensesForApplicableQuarterEndNetAssetValue
Namespace Prefix:	klcc_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount of reimbursement payment obligation under the expense support and conditional reimbursement agreement.

+ References

No definition available.

+ Details

Name:	klcc_ReimbursementPaymentObligation
Namespace Prefix:	klcc_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Period to reimburse payment, in P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

+ References

No definition available.

+ Details

Name:	klcc_ReimbursementPaymentPeriod
Namespace Prefix:	klcc_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Period to reimburse the expense payments, in PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

+ References

No definition available.

+ Details

Name:	klcc_ReimbursementPeriodOfExpensePayments
Namespace Prefix:	klcc_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

The amount of additional expense support provided by related party.

+ References

No definition available.

+ Details

Name:	klcc_RelatedPartyAdditionalExpenseSupport
Namespace Prefix:	klcc_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Details

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Data Type:	na
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- Details

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