The additional amount available over and above the maximum borrowing capacity under the credit facility.

No definition available.

Name:	kai_LineOfCreditFacilityAdditionalBorrowingCapacity
Namespace Prefix:	kai_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

The maximum amount of unrestricted U.S. cash that can be netted against total debt.

+ References

No definition available.

+ Details

Name:	kai_LineOfCreditFacilityMaximumUnrestrictedDomesticCash
Namespace Prefix:	kai_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

The maximum consolidated leverage ratio under the negative covenants of the credit facility.

+ References

No definition available.

+ Details

Name:	kai_MaximumConsolidatedLeverageRatio
Namespace Prefix:	kai_
Data Type:	xbrli:pureItemType
Balance Type:	na
Period Type:	duration

- Definition

Maximum Consolidated Leverage Ratio Upon Material Acquisition

+ References

No definition available.

+ Details

Name:	kai_MaximumConsolidatedLeverageRatioUponMaterialAcquisition
Namespace Prefix:	kai_
Data Type:	xbrli:pureItemType
Balance Type:	na
Period Type:	duration

- Definition

Noncash Purchase Of Property, Previous Outstanding Loan Receivable Applied

+ References

No definition available.

+ Details

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

- Definition

Amount of consideration transferred in asset acquisition. Includes, but is not limited to, cash, liability incurred by acquirer, and equity interest issued by acquirer.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 805
-SubTopic 50
-Section 30
-Paragraph 2
-URI https://asc.fasb.org/extlink&oid=126928898&loc=d3e9215-128498

Reference 2: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 805
-SubTopic 50
-Section 55
-Paragraph 1
-URI https://asc.fasb.org/extlink&oid=6829253&loc=SL6831962-166255

Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 805
-SubTopic 50
-Section 25
-Paragraph 1
-URI https://asc.fasb.org/extlink&oid=127000608&loc=d3e9135-128495

Reference 4: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 805
-SubTopic 50
-Section 30
-Paragraph 1
-URI https://asc.fasb.org/extlink&oid=126928898&loc=d3e9212-128498

+ Details

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

- Definition

Amount of debt and lease obligation, classified as current.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(21))
-URI https://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

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

- Definition

Percentage points added to the reference rate to compute the variable rate on the debt instrument.

+ References

No definition available.

+ Details

Name:	us-gaap_DebtInstrumentBasisSpreadOnVariableRate1
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Face (par) amount of debt instrument at time of issuance.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 50
-Paragraph 1B
-Subparagraph (a)
-URI https://asc.fasb.org/extlink&oid=123466505&loc=SL123495323-112611

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 835
-SubTopic 30
-Section 45
-Paragraph 2
-URI https://asc.fasb.org/extlink&oid=124435984&loc=d3e28551-108399

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 835
-SubTopic 30
-Section 55
-Paragraph 8
-URI https://asc.fasb.org/extlink&oid=114775985&loc=d3e28878-108400

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 835
-SubTopic 30
-Section 50
-Paragraph 1
-URI https://asc.fasb.org/extlink&oid=124429444&loc=SL124452920-239629

Reference 5: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 55
-Paragraph 69C
-URI https://asc.fasb.org/extlink&oid=123466577&loc=SL123495737-112612

Reference 6: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 55
-Paragraph 69B
-URI https://asc.fasb.org/extlink&oid=123466577&loc=SL123495735-112612

+ Details

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

- Definition

Effective interest rate for the funds borrowed under the debt agreement considering interest compounding and original issue discount or premium.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 50
-Paragraph 6
-Subparagraph (a)
-URI https://asc.fasb.org/extlink&oid=123466204&loc=SL6036836-161870

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 835
-SubTopic 30
-Section 45
-Paragraph 2
-URI https://asc.fasb.org/extlink&oid=124435984&loc=d3e28551-108399

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 835
-SubTopic 30
-Section 50
-Paragraph 1
-URI https://asc.fasb.org/extlink&oid=124429444&loc=SL124452920-239629

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.22(a)(1))
-URI https://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

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

- Definition

Contractual interest rate for funds borrowed, under the debt agreement.

+ References

+ Details

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

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

- Definition

The fee, expressed as a percentage of the line of credit facility, for the line of credit facility regardless of whether the facility has been used.

+ References

No definition available.

+ Details

Name:	us-gaap_LineOfCreditFacilityCommitmentFeePercentage
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Maximum borrowing capacity under the credit facility without consideration of any current restrictions on the amount that could be borrowed or the amounts currently outstanding under the facility.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.19(b),22(b))
-URI https://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

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

- Definition

Amount of borrowing capacity currently available under the credit facility (current borrowing capacity less the amount of borrowings outstanding).

+ References

+ Details

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

- Definition

Amount, excluding unamortized premium (discount) and debt issuance cost, of long-term debt. Excludes lease obligation.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 50
-Paragraph 4
-Subparagraph (b)(3)
-URI https://asc.fasb.org/extlink&oid=123466204&loc=SL6031897-161870

Reference 2: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 55
-Paragraph 69C
-URI https://asc.fasb.org/extlink&oid=123466577&loc=SL123495737-112612

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 944
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03(a)(16))
-URI https://asc.fasb.org/extlink&oid=126734703&loc=d3e572229-122910

Reference 4: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 55
-Paragraph 69B
-URI https://asc.fasb.org/extlink&oid=123466577&loc=SL123495735-112612

Reference 5: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(16))
-URI https://asc.fasb.org/extlink&oid=126897435&loc=d3e534808-122878

Reference 6: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 50
-Paragraph 1D
-Subparagraph (b)
-URI https://asc.fasb.org/extlink&oid=123466505&loc=SL123495340-112611

Reference 7: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(22))
-URI https://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

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

- Definition

Weighted average interest rate of long-term debt outstanding calculated at point in time.

+ References

No definition available.

+ Details

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

- Definition

Reflects the total carrying amount as of the balance sheet date of debt having initial terms less than one year or the normal operating cycle, if longer.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 852
-SubTopic 10
-Section 55
-Paragraph 10
-URI https://asc.fasb.org/extlink&oid=84165509&loc=d3e56426-112766

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(19)(a))
-URI https://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 944
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03(a)(16)(a)(1))
-URI https://asc.fasb.org/extlink&oid=126734703&loc=d3e572229-122910

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(13))
-URI https://asc.fasb.org/extlink&oid=126897435&loc=d3e534808-122878

+ Details

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

- Details

Name:	us-gaap_AssetAcquisitionAxis=kai_FacilityMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_BusinessAcquisitionAxis=kai_TheClouthGroupOfCompaniesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_RangeAxis=srt_MaximumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=us-gaap_LineOfCreditMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=kai_TwoThousandSeventeenCreditAgreementMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=kai_SixthAmendmentToUnsecuredMultiCurrencyRevolvingCreditFacilityCreditAgreementMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=kai_SixthAmendmentToUnsecuredMultiCurrencyRevolvingCreditFacilityEuroDenominatedBorrowingMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_RangeAxis=srt_MinimumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_CreditFacilityAxis=us-gaap_RevolvingCreditFacilityMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_VariableRateAxis=us-gaap_BaseRateMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_VariableRateAxis=kai_EurocurrencyRateTermSOFRCDORRateAndRFRMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=us-gaap_SeniorNotesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=kai_NotePurchaseAgreementMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Short- and Long-Term Obligations - Additional Information (Details) € in Thousands		1 Months Ended		12 Months Ended
	Nov. 30, 2022 USD ($)	Aug. 31, 2022 USD ($)	Aug. 31, 2022 EUR (€)	Dec. 31, 2022 USD ($)	Jan. 01, 2022 USD ($)	Jan. 02, 2021 USD ($)	Dec. 29, 2018 USD ($)	Mar. 01, 2017 USD ($)
Debt Instrument [Line Items]
Short-and long-term debt, excluding finance leases				$ 199,221,000
Current maturities of long-term obligations				3,821,000	$ 5,356,000
Purchase of property with outstanding loan receivable				1,397,000	0	$ 0
Facility
Debt Instrument [Line Items]
Consideration transferred for asset acquisition		$ 2,730,000	€ 2,722
Purchase of property with outstanding loan receivable		$ 1,397,000	€ 1,393
Clouth
Debt Instrument [Line Items]
Short-and long-term debt, excluding finance leases				1,920,000
Short-term debt				$ 665,000
Maximum \| Clouth
Debt Instrument [Line Items]
Effective interest rate				1.70%
Revolving credit facility
Debt Instrument [Line Items]
Short-and long-term debt, excluding finance leases				$ 186,131,000	$ 250,267,000
Weighted average interest rate for long-term obligations				4.33%	1.50%
Revolving credit facility \| 2017 Credit Agreement
Debt Instrument [Line Items]
Uncommitted unsecured additional borrowing capacity								$ 150,000,000
Revolving credit facility \| Credit Agreement
Debt Instrument [Line Items]
Uncommitted unsecured additional borrowing capacity	$ 200,000,000			$ 200,000,000
Borrowing capacity available under committed portion	400,000,000
Maximum amount of unrestricted U.S. cash	$ 50,000,000
Maximum consolidated leverage ratio	3.75
Maximum consolidated leverage ratio upon material acquisition	4.25
Short-and long-term debt, excluding finance leases				186,131,000
Remaining borrowing capacity				214,061,000
Revolving credit facility \| Euro-Denominated Borrowing
Debt Instrument [Line Items]
Short-and long-term debt, excluding finance leases				73,131,000
Revolving credit facility \| Minimum \| Credit Agreement \| Revolving Credit Facility
Debt Instrument [Line Items]
Commitment fee percentage	0.125%
Revolving credit facility \| Maximum \| Credit Agreement \| Revolving Credit Facility
Debt Instrument [Line Items]
Commitment fee percentage	0.35%
Revolving credit facility \| Base Rate \| Minimum \| Credit Agreement
Debt Instrument [Line Items]
Basis spread on variable rate (as a percentage)	0.00%
Revolving credit facility \| Base Rate \| Maximum \| Credit Agreement
Debt Instrument [Line Items]
Basis spread on variable rate (as a percentage)	1.25%
Revolving credit facility \| Eurocurrency Rate, Term SOFR, CDOR Rate, and RFR \| Credit Agreement
Debt Instrument [Line Items]
Basis spread on variable rate (as a percentage)	0.10%
Revolving credit facility \| Eurocurrency Rate, Term SOFR, CDOR Rate, and RFR \| Minimum \| Credit Agreement
Debt Instrument [Line Items]
Basis spread on variable rate (as a percentage)	1.00%
Revolving credit facility \| Eurocurrency Rate, Term SOFR, CDOR Rate, and RFR \| Maximum \| Credit Agreement
Debt Instrument [Line Items]
Basis spread on variable rate (as a percentage)	2.25%
Senior promissory notes
Debt Instrument [Line Items]
Short-and long-term debt, excluding finance leases				10,000,000	$ 10,000,000
Senior promissory notes \| Note Purchase Agreement
Debt Instrument [Line Items]
Principal amount							$ 10,000,000
Fixed interest rate							4.90%
Current maturities of long-term obligations				$ 1,670,000