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Revenue from Contracts with Customers - Contract Assets and Contract Liabilities (Details) - USD ($) $ in Millions		3 Months Ended	9 Months Ended
	Jul. 19, 2021	Feb. 26, 2022	Feb. 26, 2022
Revenue from Contract with Customer [Abstract]
Contract with customer, liability, net sales		$ 14.2	$ 85.5
Contract with customer, liability, increase (decrease) for contract acquired in business combination	$ 55.5

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- Definition

Contract with Customer, Liability, Revenue Recognized in Period

+ References

No definition available.

+ Details

Name:	mlkn_ContractWithCustomerLiabilityRevenueRecognizedInPeriod
Namespace Prefix:	mlkn_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

X

- Definition

Amount of increase (decrease) in obligation to transfer good or service to customer for which consideration from customer has been received or is due, from business combination.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 50
-Paragraph 10
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=123351226&loc=SL49130551-203045

+ Details

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

X

- References

No definition available.

+ Details

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