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Revenue from Contracts with Customers - Contract Assets and Contract Liabilities (Details) - USD ($) $ in Millions |  | 3 Months Ended | 6 Months Ended
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Jul. 19, 2021 | Nov. 27, 2021 | Nov. 27, 2021
Revenue from Contract with Customer [Abstract] |  |  |
Contract with customer, liability, net sales |  | $ 30.2 | $ 71.3
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

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- 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

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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