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Revenue from Contracts with Customers - Contract Assets and Contract Liabilities (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Dec. 03, 2022	Nov. 27, 2021	Dec. 03, 2022	Nov. 27, 2021
Revenue from Contract with Customer [Abstract]
Contract with customer, liability, net sales	$ 104.8	$ 25.7	$ 104.8	$ 25.7

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- Definition

Contract with Customer, Liability, Revenue Recognized In Period

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No definition available.

+ Details

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

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- References

No definition available.

+ Details

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