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Commitments and Contingencies (Details) - USD ($) $ in Thousands | 9 Months Ended |
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Sep. 28, 2024 | Dec. 30, 2023
Commitments and Contingencies Disclosure [Abstract] |  |
Banker's acceptance drafts, maturity period (in months) | 6 months |
Banker's acceptance drafts with recourse | $ 10,476 | $ 9,090

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- Definition Bank Acceptance, Maturity Period + References No definition available. + Details
Name: | kai_BankAcceptanceMaturityPeriod
Namespace Prefix: | kai_
Data Type: | xbrli:durationItemType
Balance Type: | na
Period Type: | duration

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- Definition The amount of the financial institution's obligation to pay the holder of the customer's draft which the financial institution has guaranteed (i.e., Banker's Acceptance). + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Topic 942 -SubTopic 210 -Name Accounting Standards Codification -Section S99 -Paragraph 1 -Subparagraph (SX 210.9-03(14)) -Publisher FASB -URI https://asc.fasb.org/1943274/2147478546/942-210-S99-1 + Details
Name: | us-gaap_BankAcceptancesExecuted
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | instant

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- References No definition available. + Details
Name: | us-gaap_CommitmentsAndContingenciesDisclosureAbstract
Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration