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Derivatives - Narrative (Details)	6 Months Ended
	Jun. 29, 2024
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

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

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

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

X

- Details

Name:	us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis=us-gaap_CashFlowHedgingMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

X

- Details

Name:	us-gaap_DerivativeInstrumentRiskAxis=us-gaap_ForeignExchangeForwardMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

X

- Details

Name:	us-gaap_HedgingDesignationAxis=us-gaap_DesignatedAsHedgingInstrumentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: