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Derivatives - Narrative (Details)	9 Months Ended
	Oct. 01, 2022 USD ($)	Dec. 29, 2018 USD ($)
Derivatives, Fair Value [Line Items]
Net unrealized gains included in AOCI expected to be reclassified to earnings over the next 12 months	$ 44,000
Cash Flow Hedging | Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Rate of effectiveness of derivative agreement	100.00%
Cash Flow Hedging | 2018 Swap Agreement | Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Derivative, notional amount		$ 15,000,000
Derivative, floor rate		0
Fixed rate of interest		3.15%
Cash Flow Hedging | Forward Currency- Exchange Contract | Designated as Hedging Instrument
Derivatives, Fair Value [Line Items]
Period over which entity manages its level of exposure of risk	12 months

X

- Definition

The period over which the entity typically manages its level of exposure to the risk of currency-exchange fluctuations by hedging a portion of its currency exposures anticipated over the ensuing period.

+ References

No definition available.

+ Details

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Namespace Prefix:	kai_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

X

- Definition

The percentage of effectiveness of derivative instruments.

+ References

No definition available.

+ Details

Name:	kai_RateOfEffectivenessOfDerivativeAgreement
Namespace Prefix:	kai_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

X

- Definition

The estimated net amount of existing gains or losses on cash flow hedges at the reporting date expected to be reclassified to earnings within the next 12 months.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 815
-SubTopic 30
-Section 50
-Paragraph 1
-Subparagraph (c)
-URI https://asc.fasb.org/extlink&oid=121549185&loc=d3e80748-113994

+ Details

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

X

- Definition

Floor rate on a foreign currency derivative for example, but not limited to, a floor or a collar.

+ References

No definition available.

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:pureItemType
Balance Type:	na
Period Type:	instant

X

- Definition

Fixed interest rate related to the interest rate derivative.

+ References

No definition available.

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

X

- Definition

Nominal or face amount used to calculate payment on derivative.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 815
-SubTopic 10
-Section 50
-Paragraph 1B
-URI https://asc.fasb.org/extlink&oid=125515794&loc=SL5580258-113959

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 815
-SubTopic 10
-Section 50
-Paragraph 1A
-Subparagraph (d)
-URI https://asc.fasb.org/extlink&oid=125515794&loc=SL5579245-113959

+ Details

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

X

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

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- Details

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- Details

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Namespace Prefix:
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X

- Details

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Namespace Prefix:
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Period Type:

X

- Details

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Namespace Prefix:
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Period Type: