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Fair Value Measurements and Fair Value of Financial Instruments - Fair Value of Assets and Liabilities Measured on a Recurring Basis (Details) - Recurring - USD ($) $ in Thousands	Apr. 02, 2022	Jan. 01, 2022
Assets:
Money market funds and time deposits	$ 14,175	$ 13,458
Banker's acceptance drafts	8,147	8,049
Forward currency-exchange contracts		14
Liabilities:
2018 Swap Agreement	179	550
Forward currency-exchange contract	66	44
Level 1
Assets:
Money market funds and time deposits	14,175	13,458
Banker's acceptance drafts	0	0
Forward currency-exchange contracts		0
Liabilities:
2018 Swap Agreement	0	0
Forward currency-exchange contract	0	0
Level 2
Assets:
Money market funds and time deposits	0	0
Banker's acceptance drafts	8,147	8,049
Forward currency-exchange contracts		14
Liabilities:
2018 Swap Agreement	179	550
Forward currency-exchange contract	66	44
Level 3
Assets:
Money market funds and time deposits	0	0
Banker's acceptance drafts	0	0
Forward currency-exchange contracts		0
Liabilities:
2018 Swap Agreement	0	0
Forward currency-exchange contract	$ 0	$ 0

X

- Definition

This element represents the portion of the balance sheet assertion valued at fair value by the entity whether such amount is presented as a separate caption or as a parenthetical disclosure. Additionally, this element may be used in connection with the fair value disclosures required in the footnote disclosures to the financial statements. The element may be used in both the balance sheet and disclosure in the same submission. Amounts receivable from customers on short-term negotiable time drafts drawn on and accepted by the institution (also known as banker's acceptance transactions) that are outstanding on the reporting date.

+ References

No definition available.

+ Details

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Namespace Prefix:	kai_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

X

- References

No definition available.

+ Details

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

X

- Definition

Fair value portion of currency on hand as well as demand deposits with banks or financial institutions. Includes other kinds of accounts that have the general characteristics of demand deposits. Also includes short-term, highly liquid investments that are both readily convertible to known amounts of cash and so near their maturity that they present insignificant risk of changes in value because of changes in interest rates.

+ References

No definition available.

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Namespace Prefix:	us-gaap_
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X

- Definition

Fair value, after the effects of master netting arrangements, of a financial liability or contract with one or more underlyings, notional amount or payment provision or both, and the contract can be net settled by means outside the contract or delivery of an asset. Includes liabilities not subject to a master netting arrangement and not elected to be offset.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 20
-Section 50
-Paragraph 3
-Subparagraph (c)
-URI http://asc.fasb.org/extlink&oid=51824906&loc=SL20225862-175312

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 20
-Section 55
-Paragraph 10
-URI http://asc.fasb.org/extlink&oid=99393222&loc=SL20226008-175313

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 825
-SubTopic 10
-Section 50
-Paragraph 10
-URI http://asc.fasb.org/extlink&oid=123594938&loc=d3e13433-108611

Reference 4: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 20
-Section 55
-Paragraph 22
-URI http://asc.fasb.org/extlink&oid=99393222&loc=SL20226052-175313

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Balance Type:	credit
Period Type:	instant

X

- Definition

Fair value portion of asset contracts related to the exchange of different currencies, including, but not limited to, foreign currency options, forward contracts, and swaps.

+ References

No definition available.

+ Details

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Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

X

- Definition

Fair value portion of liability contracts related to the exchange of different currencies, including, but not limited to, foreign currency options, forward (delivery or nondelivery) contracts, and swaps entered into.

+ References

No definition available.

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Namespace Prefix:	us-gaap_
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Balance Type:	credit
Period Type:	instant

X

- References

No definition available.

+ Details

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

X

- Details

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- Details

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