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Commitments and Contingencies (Details) - USD ($) $ in Thousands	3 Months Ended
	Apr. 04, 2026	Jan. 03, 2026
Commitments and Contingencies Disclosure [Abstract]
Banker's acceptance drafts, maturity period (in months)	6 months
Banker's acceptance drafts with recourse	$ 8,482	$ 9,556

X

- 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

X

- 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://www.xbrl.org/2009/role/commonPracticeRef
-Topic 942
-SubTopic 210
-Name Accounting Standards Codification
-Section S45
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477657/942-210-S45-1

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 942
-SubTopic 210
-Name Accounting Standards Codification
-Section S50
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478478/942-210-S50-1

Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-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

X

- References

No definition available.

+ Details

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