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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 + References No definition available. + Details
Name: | mlkn_ContractWithCustomerLiabilityRevenueRecognizedInPeriod
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