Amount of cash payments made as the result of exit or disposal activities. Excludes payments associated with a discontinued operation or an asset retirement obligation.

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 420
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (b)(2)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482017/420-10-50-1

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 230
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 17
-Subparagraph (f)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482740/230-10-45-17

+ Details

Name:	us-gaap_PaymentsForRestructuring
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount of expenses associated with exit or disposal activities pursuant to an authorized plan. Excludes expenses related to a discontinued operation or an asset retirement obligation.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section 45
-Paragraph 28
-Subparagraph (b)
-SubTopic 10
-Topic 230
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482740/230-10-45-28

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 420
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Subparagraph (SAB Topic 5.P.4(b)(1))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479823/420-10-S99-2

Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 420
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 3
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482047/420-10-45-3

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 420
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SAB Topic 5.P.3)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479823/420-10-S99-1

+ Details

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

- Definition

Carrying amount (including both current and noncurrent portions of the accrual) as of the balance sheet date pertaining to a specified type of cost associated with exit from or disposal of business activities or restructuring pursuant to a duly authorized plan.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 420
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (b)(2)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482017/420-10-50-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 420
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Subparagraph (SAB TOPIC 5.P.4(b)(2))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479823/420-10-S99-2

+ Details

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

- Definition

Amount of increase (decrease) in cumulative translation adjustment, after tax, from translating foreign currency financial statements into the reporting currency.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 220
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 11
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482790/220-10-45-11

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 830
-SubTopic 30
-Name Accounting Standards Codification
-Section 45
-Paragraph 20
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481694/830-30-45-20

+ Details

Name:	us-gaap_TranslationAdjustmentFunctionalToReportingCurrencyNetOfTaxPeriodIncreaseDecrease
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	na
Period Type:	duration

- Details

Name:	us-gaap_RestructuringPlanAxis=kai_A2021RestructuringPlanMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_RestructuringCostAndReserveAxis=us-gaap_EmployeeSeveranceMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_RestructuringCostAndReserveAxis=kai_FacilityAndOtherClosureCostsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_RestructuringPlanAxis=kai_A2023RestructuringPlanMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Gain on Sale and Other Costs, Net - Summary of Changes in Accrued Restructuring Costs Included in Other Current Liabilities (Details) - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	Sep. 30, 2023	Oct. 01, 2022	Sep. 30, 2023	Oct. 01, 2022
Restructuring Reserve [Roll Forward]
Provision	$ 398	$ 72	$ 398	$ 72
2021 Restructuring Plan
Restructuring Reserve [Roll Forward]
Beginning balance			389
Usage			(386)
Currency translation			(3)
Ending balance	0		0
2021 Restructuring Plan \| Severance Costs
Restructuring Reserve [Roll Forward]
Beginning balance			189
Usage			(187)
Currency translation			(2)
Ending balance	0		0
2021 Restructuring Plan \| Facility and Other Closure Costs
Restructuring Reserve [Roll Forward]
Beginning balance			200
Usage			(199)
Currency translation			(1)
Ending balance	0		0
2023 Restructuring Plan
Restructuring Reserve [Roll Forward]
Provision			398
Usage			(23)
Currency translation			(11)
Ending balance	364		364
2023 Restructuring Plan \| Severance Costs
Restructuring Reserve [Roll Forward]
Provision			369
Usage			(23)
Currency translation			(10)
Ending balance	336		336
2023 Restructuring Plan \| Facility and Other Closure Costs
Restructuring Reserve [Roll Forward]
Provision			29
Usage			0
Currency translation			(1)
Ending balance	$ 28		$ 28