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Revenue from Contracts with Customers - Contract Assets and Contract Liabilities (Details) - USD ($) $ in Millions | 3 Months Ended
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Sep. 03, 2022 | Aug. 28, 2021
Revenue from Contract with Customer [Abstract] |  |
Contract with customer, liability, net sales | $ 79.1 | $ 41.1

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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