Percentage of voting equity interest acquired in business combination.

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

- Definition

The percentage of ownership of common stock or equity participation in the investee accounted for under the equity method of accounting.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 825
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 28
-Subparagraph (f)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482907/825-10-50-28

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 323
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (a)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481687/323-10-50-3

+ Details

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

- Definition

Amount of the entity's equity method investment which has been sold.

+ References

No definition available.

+ Details

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

- Definition

The designation of funds furnished by a borrower to a lender to assure future payments of the borrower's real estate taxes and insurance obligations with respect to a mortgaged property. Escrow deposits may be made for a variety of other purposes such as earnest money and contingent payments. This element excludes replacement reserves which are an escrow separately provided for within the US GAAP taxonomy.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 942
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(10))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478546/942-210-S99-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 954
-SubTopic 440
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (d)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478522/954-440-50-1

+ Details

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

- Definition

Amount of income (loss) for proportionate share of equity method investee's income (loss).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section 45
-Paragraph 28
-Subparagraph (b)
-SubTopic 10
-Topic 230
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482740/230-10-45-28

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 270
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (i)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482964/270-10-50-1

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 280
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 32
-Subparagraph (ee)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482810/280-10-50-32

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 944
-SubTopic 220
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-04(10))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477250/944-220-S99-1

Reference 5: http://www.xbrl.org/2003/role/disclosureRef
-Topic 323
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481664/323-10-45-1

Reference 6: http://www.xbrl.org/2003/role/disclosureRef
-Topic 280
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 22
-Subparagraph (g)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482810/280-10-50-22

Reference 7: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 220
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Subparagraph (SX 210.5-03(12))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147483621/220-10-S99-2

Reference 8: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 942
-SubTopic 220
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-04(13)(f))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478524/942-220-S99-1

+ Details

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

- Definition

The parent entity's interest in net assets of the subsidiary, expressed as a percentage.

+ References

No definition available.

+ Details

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

- Definition

Amortized cost, before allowance for credit loss, of financing receivable. Excludes financing receivable covered under loss sharing agreement and net investment in lease.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 326
-SubTopic 20
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479344/326-20-45-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 825
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 1A
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482736/825-10-45-1A

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 948
-SubTopic 310
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477011/948-310-45-1

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 310
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 13
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481990/310-10-45-13

Reference 5: http://fasb.org/us-gaap/role/ref/otherTransitionRef
-Topic 310
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 7A
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481962/310-10-50-7A

Reference 6: http://fasb.org/us-gaap/role/ref/otherTransitionRef
-Topic 310
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 29
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481962/310-10-50-29

Reference 7: http://www.xbrl.org/2003/role/disclosureRef
-Name Regulation S-K (SK)
-Number 229
-Section 1405
-Paragraph a
-Subparagraph (1)
-Publisher SEC

Reference 8: http://www.xbrl.org/2003/role/disclosureRef
-Name Regulation S-K (SK)
-Number 229
-Section 1405
-Paragraph a
-Subparagraph (2)
-Publisher SEC

Reference 9: http://www.xbrl.org/2009/role/commonPracticeRef
-Name Regulation S-K (SK)
-Number 229
-Section 1404
-Paragraph a
-Publisher SEC

Reference 10: http://www.xbrl.org/2003/role/exampleRef
-Topic 326
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 80
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479294/326-20-55-80

Reference 11: http://www.xbrl.org/2003/role/exampleRef
-Topic 326
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 79
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479294/326-20-55-79

Reference 12: http://www.xbrl.org/2003/role/disclosureRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(3)(b))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

Reference 13: http://www.xbrl.org/2003/role/disclosureRef
-Topic 326
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 14
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479319/326-20-50-14

Reference 14: http://www.xbrl.org/2003/role/disclosureRef
-Topic 326
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 5
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479319/326-20-50-5

+ Details

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

- Definition

The cash outflow associated with the acquisition of business during the period. The cash portion only of the acquisition price.

+ 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 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479581/805-30-50-2

Reference 4: 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 5: 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_PaymentsToAcquireBusinessesGross
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

The cash inflow associated with the sale of equity method investments, which are investments in joint ventures and entities in which the entity has an equity ownership interest normally of 20 to 50 percent and exercises significant influence.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 12
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482740/230-10-45-12

+ Details

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

- 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 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S50
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480738/235-10-S50-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 825
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 28
-Subparagraph (f)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482907/825-10-50-28

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.4-08(g)(1)(ii))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480678/235-10-S99-1

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 323
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481687/323-10-50-3

Reference 5: http://www.xbrl.org/2003/role/disclosureRef
-Topic 323
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (a)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481687/323-10-50-3

Reference 6: http://www.xbrl.org/2003/role/disclosureRef
-Topic 323
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (a)(2)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481687/323-10-50-3

Reference 7: http://www.xbrl.org/2003/role/disclosureRef
-Topic 323
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481687/323-10-50-3

+ Details

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

- Details

Name:	dei_LegalEntityAxis=mlkn_GlobalHoldingsNetherlandsB.V.Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_OwnershipAxis=mlkn_MAARSMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis=mlkn_GlobalHoldingsNetherlandsB.V.Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_BusinessAcquisitionAxis=mlkn_GlobalHoldingsNetherlandsB.V.Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Investments in Nonconsolidated Affiliates - Narrative (Details) - USD ($) $ in Millions			12 Months Ended
	Oct. 30, 2023	Aug. 31, 2018	May 31, 2025	Jun. 01, 2024	Jun. 03, 2023
Schedule of Equity Method Investments
Proceeds from the sale of equity method investment			$ 0.0	$ 3.5	$ 0.0
Loss on sale of equity method investment			$ 0.0	$ 0.4	$ 0.0
Global Holdings Netherlands B.V. (Maars) \| MAARS
Schedule of Equity Method Investments
Ownership interest (as percent)		100.00%
Global Holdings Netherlands B.V. (Maars)
Schedule of Equity Method Investments
Ownership interest (as percent)	48.20%
Equity method investment, amount sold	$ 5.9
Proceeds from the sale of equity method investment	3.5
Vendor loan receivable	1.4
Cash in escrow	$ 0.9
Global Holdings Netherlands B.V. (Maars)
Schedule of Equity Method Investments
Outstanding equity interest acquired (as percent)		48.20%
Cash payment to acquire equity interest		$ 6.1