Nature of Operations and Summary of Significant Accounting Policies - Changes in the Allowance for Credit Losses (Details) - USD ($) $ in Thousands	12 Months Ended
Jan. 01, 2022	Jan. 02, 2021	Dec. 28, 2019
Accounts Receivable, Allowance for Credit Loss [Roll Forward]
Balance at Beginning of Year	$ 2,977	$ 2,698	$ 2,897
Provision charged to expense	5	356	114
Accounts written off	(178)	(266)	(263)
Currency translation	(69)	189	(50)
Balance at End of Year	$ 2,735	$ 2,977	$ 2,698

Allowance For Doubtful Accounts Receivable, Currency Translation Increase (Decrease)

No definition available.

Name:	kai_AllowanceForDoubtfulAccountsReceivableCurrencyTranslationIncreaseDecrease
Namespace Prefix:	kai_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount of allowance for credit loss on accounts receivable.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 326
-SubTopic 20
-Section 50
-Paragraph 13
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=124255953&loc=SL82919249-210447

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 310
-SubTopic 10
-Section 50
-Paragraph 4
-URI http://asc.fasb.org/extlink&oid=123577603&loc=d3e5074-111524

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 326
-SubTopic 20
-Section 50
-Paragraph 13
-Subparagraph (f)
-URI http://asc.fasb.org/extlink&oid=124255953&loc=SL82919249-210447

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 326
-SubTopic 20
-Section 45
-Paragraph 1
-URI http://asc.fasb.org/extlink&oid=124255206&loc=SL82895884-210446

+ Details

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

- Definition

A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

+ References

No definition available.

+ Details

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

- Definition

Amount of direct write-downs of accounts receivable charged against the allowance.

+ References

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Amount of expense (reversal of expense) for expected credit loss on accounts receivable.

+ References

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration