Restructuring - Narrative (Details) - USD ($) $ in Millions	3 Months Ended	6 Months Ended
Oct. 28, 2023	Oct. 28, 2023	Oct. 29, 2022
Restructuring Cost And Reserve [Line Items]
Asset impairment charges		$ 0.6	$ 0.4
Restructuring liability	$ 0.1	0.1
Automotive
Restructuring Cost And Reserve [Line Items]
Severance costs	0.2	0.2
Selling and Administrative Expenses
Restructuring Cost And Reserve [Line Items]
Severance costs	$ 0.4	$ 0.5

The aggregate amount of write-downs for impairments recognized during the period for long lived assets held for use (including those held for disposal by means other than sale).

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section 45
-Paragraph 28
-Subparagraph (b)
-SubTopic 10
-Topic 230
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482740/230-10-45-28

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 360
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482099/360-10-50-2

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 360
-SubTopic 10
-Section 45
-Paragraph 4
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482130/360-10-45-4

+ Details

Name:	us-gaap_ImpairmentOfLongLivedAssetsHeldForUse
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- 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

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 420
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482017/420-10-50-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 420
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (b)(2)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482017/420-10-50-1

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 420
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (b)(1)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482017/420-10-50-1

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 420
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Subparagraph (SAB Topic 5.P.4(b)(2))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479823/420-10-S99-2

Reference 5: http://www.xbrl.org/2003/role/disclosureRef
-Topic 420
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Subparagraph (SAB Topic 5.P.4(b)(1))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479823/420-10-S99-2

Reference 6: http://www.xbrl.org/2003/role/disclosureRef
-Topic 420
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Subparagraph (SAB Topic 5.P.4(d))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479823/420-10-S99-2

Reference 7: http://www.xbrl.org/2003/role/disclosureRef
-Topic 420
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (d)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482017/420-10-50-1

+ Details

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

- Definition

Carrying amount (including both current and noncurrent portions of the accrual) as of the balance sheet date pertaining to a specified type of cost associated with exit from or disposal of business activities or restructuring pursuant to a duly authorized plan.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 420
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (b)(2)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482017/420-10-50-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 420
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Subparagraph (SAB TOPIC 5.P.4(b)(2))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479823/420-10-S99-2

+ Details

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

- Definition

Amount of expenses for special or contractual termination benefits provided to current employees involuntarily terminated under a benefit arrangement associated exit or disposal activities pursuant to an authorized plan. Excludes expenses related to one-time termination benefits, a discontinued operation or an asset retirement obligation.

+ References

+ Details

Name:	us-gaap_SeveranceCosts1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Details

Name:	us-gaap_StatementBusinessSegmentsAxis=mei_AutomotiveMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_ProductOrServiceAxis=mei_SellingAndAdministrativeExpensesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: