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Significant Accounting and Reporting Policies - Schedule of Self Insurance (Details) - USD ($) $ in Thousands	May 31, 2025	Jun. 01, 2024
Accounting Policies [Abstract]
General liability	$ 1,000
Auto liability	1,000
Workers' compensation	750
Health benefit	700
Self-insurance arrangements liability	$ 13,100	$ 12,000

X

- Definition

Self Insurance, Retention Level, Auto Liability

+ References

No definition available.

+ Details

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Data Type:	xbrli:monetaryItemType
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X

- Definition

Self Insurance, Retention Level, General Liability

+ References

No definition available.

+ Details

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Namespace Prefix:	mlkn_
Data Type:	xbrli:monetaryItemType
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X

- Definition

Self Insurance, Retention Level, Health Benefit

+ References

No definition available.

+ Details

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Namespace Prefix:	mlkn_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

X

- Definition

Self Insurance, Retention Level, Workers Compensation

+ References

No definition available.

+ Details

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Namespace Prefix:	mlkn_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
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X

- References

No definition available.

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X

- Definition

Liability as of the balance sheet date for amounts representing estimated cost of settling unpaid claims under the terms of the underlying insurance policies, less estimated reinsurance recoveries on such claims. This includes an estimate for claims which have been incurred but not reported. Claim adjustment expenses represent the costs estimated to be incurred in the settlement of unpaid claims.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 944
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03(a)(13)(a)(1))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478777/944-210-S99-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 944
-SubTopic 40
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (cc)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480081/944-40-50-3

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 944
-SubTopic 40
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480081/944-40-50-3

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