Dividend or interest rate associated with the financial instrument issued in exchange for the original debt being converted in a noncash or part noncash transaction. Noncash are transactions that affect recognized assets or liabilities but that do not result in cash receipts or cash payments. Part noncash refers to that portion of the transaction not resulting in cash receipts or cash payments.

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 50
-Paragraph 3
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482913/230-10-50-3

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 50
-Paragraph 5
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482913/230-10-50-5

+ Details

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

- Definition

Nominal or face amount used to calculate payments on the derivative asset.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 320
-Name Accounting Standards Codification
-Section S99
-Paragraph 5
-Subparagraph (SX 210.12-13(Column A)(Footnote 3))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480032/946-320-S99-5

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 320
-Name Accounting Standards Codification
-Section S99
-Paragraph 5C
-Subparagraph (SX 210.12-13C(Column E))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480032/946-320-S99-5C

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 320
-Name Accounting Standards Codification
-Section S99
-Paragraph 5A
-Subparagraph (SX 210.12-13A(Column D))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480032/946-320-S99-5A

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 320
-Name Accounting Standards Codification
-Section S99
-Paragraph 5B
-Subparagraph (SX 210.12-13B(Column B))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480032/946-320-S99-5B

Reference 5: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 815
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1B
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480434/815-10-50-1B

Reference 6: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 815
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1A
-Subparagraph (d)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480434/815-10-50-1A

Reference 7: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 815
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1A
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480434/815-10-50-1A

+ Details

Name:	us-gaap_DerivativeAssetNotionalAmount
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
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

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 815
-SubTopic 40
-Name Accounting Standards Codification
-Section 50
-Paragraph 5
-Subparagraph (f)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480237/815-40-50-5

+ Details

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

- Definition

Amount, after tax and reclassification, of gain (loss) from derivative instrument designated and qualifying as cash flow hedge included in assessment of hedge effectiveness.

+ References

+ Details

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

- Definition

Amount, before tax, of reclassification of gain (loss) from accumulated other comprehensive income (AOCI) for derivative instrument designated and qualifying as cash flow hedge included in assessment of hedge effectiveness.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 220
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 11
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482790/220-10-45-11

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 220
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 15
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482790/220-10-45-15

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Name Accounting Standards Codification
-Section 50
-Paragraph 4C
-Subparagraph (c)
-SubTopic 10
-Topic 815
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480434/815-10-50-4C

+ Details

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

- Details

Name:	us-gaap_DerivativeInstrumentRiskAxis=mlkn_September2016InterestRateSwapMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DerivativeInstrumentRiskAxis=mlkn_June2017InterestRateSwapMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DerivativeInstrumentRiskAxis=mlkn_January2022InterestRateSwapMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DerivativeInstrumentRiskAxis=mlkn_March2023InterestRateSwapMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Fair Value Measurements - Interest Rate Swap (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Mar. 02, 2024	Mar. 04, 2023	Mar. 02, 2024	Mar. 04, 2023
Derivative [Line Items]
(Loss) Gain recognized in Other comprehensive loss (income) (effective portion)	$ (1.1)	$ 10.3	$ (1.2)	$ 31.8
Gain reclassified from Accumulated other comprehensive loss into earnings	7.9	$ 4.9	23.0	$ 6.9
September 2016 Interest Rate Swap
Derivative [Line Items]
Notional Amount	150.0		$ 150.0
Effective Fixed Interest Rate			1.91%
June 2017 Interest Rate Swap
Derivative [Line Items]
Notional Amount	75.0		$ 75.0
Effective Fixed Interest Rate			2.348%
January 2022 Interest Rate Swap
Derivative [Line Items]
Notional Amount	575.0		$ 575.0
Effective Fixed Interest Rate			1.65%
March 2023 Interest Rate Swap
Derivative [Line Items]
Notional Amount	$ 150.0		$ 150.0
Effective Fixed Interest Rate			3.95%