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Long-Term Debt Debt (Details) - USD ($) $ in Millions		12 Months Ended
	Jan. 03, 2018	Jun. 01, 2019	Jun. 02, 2018
Line of Credit Facility
Proceeds from Issuance of Debt	$ 225.0
Repayments of Debt	$ 150.0
Long-term Debt		$ 281.9	$ 275.0
Interest Coverage		400.00%
Lessee, Finance Lease, Discount Rate		2.90%
Finance Leased Assets, Gross		$ 6.7	7.0
Long-term Construction Loan, Noncurrent		$ 6.9	7.0
Minimum
Line of Credit Facility
Leverage Ratio		350.00%
Maximum
Line of Credit Facility
Leverage Ratio		400.00%
Revolving Line of Credit, Domestic
Line of Credit Facility
Line of Credit Facility, Maximum Borrowing Capacity		$ 400.0
Line of Credit Facility, Expansion Feature, Additional Borrowing Capacity		200.0
Long-term Debt		225.0	225.0
Line of Credit Facility, Remaining Borrowing Capacity		165.0	166.8
Letters of Credit Outstanding, Amount		$ 10.0	$ 8.2

X

- Definition

Finance Leased Assets, Gross

+ References

No definition available.

+ Details

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Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

X

- Definition

Interest Coverage

+ References

No definition available.

+ Details

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Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Leverage Ratio

+ References

No definition available.

+ Details

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Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Line of Credit Facility, Expansion Feature, Additional Borrowing Capacity

+ References

No definition available.

+ Details

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Namespace Prefix:	mlhr_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

X

- Definition

This element represents the noncurrent portion of a long-term real estate loan to finance building costs. The funds are disbursed as needed or in accordance with a prearranged plan; generally, a portion of the funds is disbursed at inception and the remainder as construction progresses. The money is repaid on completion of the project (generally one to seven years), usually from the proceeds of a mortgage loan. The rate is normally higher than the prime rate, and there is usually an origination fee. The effective yield on these loans tends to be high, and the lender has a security interest in the real property.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.22)
-URI http://asc.fasb.org/extlink&oid=6877327&loc=d3e13212-122682

+ Details

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Namespace Prefix:	us-gaap_
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Balance Type:	credit
Period Type:	instant

X

- Definition

Discount rate used by lessee to determine present value of finance lease payments.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 50
-Paragraph 3
-Subparagraph (c)(3)
-URI http://asc.fasb.org/extlink&oid=77888426&loc=SL77918673-209980

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Data Type:	num:percentItemType
Balance Type:	na
Period Type:	instant

X

- Definition

The total amount of the contingent obligation under letters of credit outstanding as of the reporting date.

+ References

No definition available.

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

X

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

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

X

- Definition

Maximum borrowing capacity under the credit facility without consideration of any current restrictions on the amount that could be borrowed or the amounts currently outstanding under the facility.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
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Balance Type:	credit
Period Type:	instant

X

- Definition

Amount of borrowing capacity currently available under the credit facility (current borrowing capacity less the amount of borrowings outstanding).

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Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.19(b),22(b))
-URI http://asc.fasb.org/extlink&oid=6877327&loc=d3e13212-122682

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
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X

- Definition

Amount, after unamortized (discount) premium and debt issuance costs, of long-term debt. Includes, but not limited to, notes payable, bonds payable, debentures, mortgage loans and commercial paper. Excludes capital lease obligations.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 50
-Paragraph 4
-Subparagraph (b)(3)
-URI http://asc.fasb.org/extlink&oid=109500613&loc=SL6031897-161870

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-Publisher FASB
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-Topic 944
-SubTopic 210
-Section S99
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Balance Type:	credit
Period Type:	instant

X

- Definition

The cash inflow during the period from additional borrowings in aggregate debt. Includes proceeds from short-term and long-term debt.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 14
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=109223946&loc=d3e3255-108585

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Balance Type:	debit
Period Type:	duration

X

- Definition

The cash outflow during the period from the repayment of aggregate short-term and long-term debt. Excludes payment of capital lease obligations.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
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-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=109223946&loc=d3e3291-108585

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

X

- Details

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- Details

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