Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Customer Deposits

No definition available.

Name:	kai_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCustomerDeposits
Namespace Prefix:	kai_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
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

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 350
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 4
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482573/350-20-50-4

Reference 2: http://www.xbrl.org/2003/role/exampleRef
-Topic 805
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 8
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479328/805-10-50-8

Reference 3: http://www.xbrl.org/2003/role/exampleRef
-Topic 805
-SubTopic 10
-Name Accounting Standards Codification
-Section 55
-Paragraph 47
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479303/805-10-55-47

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 5
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479907/805-20-50-5

Reference 5: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (f)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479581/805-30-50-1

Reference 6: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (d)(1)(i)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479907/805-20-50-1

Reference 7: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (d)(1)(ii)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479907/805-20-50-1

Reference 8: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (b)(3)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479581/805-30-50-1

Reference 9: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (b)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479581/805-30-50-1

Reference 10: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 805
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (d)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479907/805-20-50-1

Reference 11: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (d)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479328/805-10-50-2

Reference 12: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479328/805-10-50-2

Reference 13: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479907/805-20-50-2

Reference 14: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479328/805-10-50-2

Reference 15: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479581/805-30-50-2

Reference 16: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479581/805-30-50-1

Reference 17: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (f)(2)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479581/805-30-50-1

Reference 18: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (e)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479907/805-20-50-1

Reference 19: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479328/805-10-50-3

Reference 20: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 4A
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479907/805-20-50-4A

Reference 21: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 4
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479907/805-20-50-4

Reference 22: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 805
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479907/805-20-50-1

Reference 23: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (b)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479907/805-20-50-1

Reference 24: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (b)(3)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479907/805-20-50-1

Reference 25: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 4A
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479907/805-20-50-4A

Reference 26: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (a)(3)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479907/805-20-50-1

Reference 27: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (a)(2)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479907/805-20-50-1

Reference 28: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 4A
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479907/805-20-50-4A

Reference 29: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 4
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479581/805-30-50-4

Reference 30: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (b)(4)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479581/805-30-50-1

Reference 31: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (b)(2)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479581/805-30-50-1

Reference 32: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479581/805-30-50-1

Reference 33: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (e)(2)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479907/805-20-50-1

Reference 34: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479907/805-20-50-1

Reference 35: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (b)(2)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479907/805-20-50-1

Reference 36: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (a)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479907/805-20-50-1

Reference 37: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 805
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (g)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479328/805-10-50-2

Reference 38: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (g)(4)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479328/805-10-50-2

Reference 39: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (g)(3)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479328/805-10-50-2

Reference 40: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (g)(2)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479328/805-10-50-2

Reference 41: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (g)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479328/805-10-50-2

Reference 42: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479328/805-10-50-2

+ Details

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

- Definition

Amount of expense for acquisition-related cost incurred to effect business combination. Includes, but is not limited to, finder's fee; advisory, legal, accounting, valuation, and other professional and consulting fees; and general administrative cost, including cost of maintaining internal acquisition department.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 805
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 7
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479328/805-10-50-7

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 805
-SubTopic 10
-Name Accounting Standards Codification
-Section 25
-Paragraph 23
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479405/805-10-25-23

+ Details

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

- Definition

Amount of asset acquired in business combination and recognized at acquisition date.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479907/805-20-50-2

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 805
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479907/805-20-50-1

+ Details

Name:	us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssets
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of cash and cash equivalent acquired in business combination and recognized at acquisition date.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 805
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479907/805-20-50-2

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 805
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479907/805-20-50-1

+ Details

Name:	us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of accounts payable assumed in business combination and recognized at acquisition date, classified as current.

+ References

+ Details

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

- Definition

Amount of identifiable intangible asset acquired in business combination and recognized at acquisition date. Excludes goodwill and financial asset.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 805
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 8
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479328/805-10-50-8

Reference 2: http://www.xbrl.org/2003/role/exampleRef
-Topic 805
-SubTopic 10
-Name Accounting Standards Codification
-Section 55
-Paragraph 41
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479303/805-10-55-41

Reference 3: http://www.xbrl.org/2003/role/exampleRef
-Topic 805
-SubTopic 10
-Name Accounting Standards Codification
-Section 55
-Paragraph 45
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479303/805-10-55-45

Reference 4: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 805
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479907/805-20-50-2

Reference 5: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 805
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479907/805-20-50-1

+ Details

Name:	us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of inventory acquired in business combination and recognized at acquisition date, classified as current.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 805
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 8
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479328/805-10-50-8

Reference 2: http://www.xbrl.org/2003/role/exampleRef
-Topic 805
-SubTopic 10
-Name Accounting Standards Codification
-Section 55
-Paragraph 41
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479303/805-10-55-41

Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 805
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479907/805-20-50-2

Reference 4: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 805
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479907/805-20-50-1

+ Details

Name:	us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedInventory
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of liability assumed in business combination and recognized at acquisition date.

+ References

+ Details

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

- Definition

Amount of property, plant, and equipment acquired in business combination and recognized at acquisition date.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 805
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 8
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479328/805-10-50-8

Reference 2: http://www.xbrl.org/2003/role/exampleRef
-Topic 805
-SubTopic 10
-Name Accounting Standards Codification
-Section 55
-Paragraph 41
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479303/805-10-55-41

Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 805
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479907/805-20-50-2

Reference 4: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 805
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479907/805-20-50-1

+ Details

Name:	us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedPropertyPlantAndEquipment
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Number of businesses acquired in business combination.

+ References

+ Details

Name:	us-gaap_NumberOfBusinessesAcquired
Namespace Prefix:	us-gaap_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	duration

- Definition

The cash outflow associated with the acquisition of a business, net of the cash acquired from the purchase.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 13
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482740/230-10-45-13

+ Details

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

- Details

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

Acquisition - Narrative (Details) $ in Thousands		3 Months Ended	9 Months Ended
Acquisition - Narrative (Details) $ in Thousands	Jul. 09, 2025 USD ($) company	Sep. 27, 2025 USD ($)	Sep. 27, 2025 USD ($)	Sep. 28, 2024 USD ($)
Business Combination [Line Items]
Acquisition costs		$ 2,253	$ 3,498
Payments to acquire business, net of cash acquired			$ 16,483	$ 302,024
Babbini
Business Combination [Line Items]
Number of businesses acquired \| company	2
Payments to acquire business, net of cash acquired	$ 16,483
Fair value of assets	35,470
Fair value of cash	4,863
Fair value of inventory	13,825
Fair value of, property, plant, and equipment	5,355
Fair value of intangible assets	5,278
Total liabilities assumed	14,124
Total liabilities assumed customer deposits	3,857
Total liabilities assumed, accounts payable	$ 2,954