Acquisitions and dispositions.

No definition available.

Name:	mei_AcquisitionsAndDispositionsLineItems
Namespace Prefix:	mei_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Disposal group including discontinued operation transaction costs.

+ References

No definition available.

+ Details

Name:	mei_DisposalGroupIncludingDiscontinuedOperationTransactionCosts
Namespace Prefix:	mei_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Gain on disposition of aircraft sale.

+ References

No definition available.

+ Details

Name:	mei_GainOnDispositionOfAircraftSale
Namespace Prefix:	mei_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount of consideration received or receivable for the disposal of assets and liabilities, including discontinued operation.

+ References

No definition available.

+ Details

Name:	us-gaap_DisposalGroupIncludingDiscontinuedOperationConsideration
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of gain (loss) on sale or disposal of assets, including but not limited to property plant and equipment, intangible assets and equity in securities of subsidiaries or equity method investee.

+ References

+ Details

Name:	us-gaap_GainLossOnDispositionOfAssets1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount of gain (loss) from sale and disposal of integrated set of activities and assets capable of being conducted and managed for purpose of providing return in form of dividend, lower cost, or other economic benefit to investor, owner, member and participant.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 230
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 28
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482740/230-10-45-28

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 810
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1B
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481203/810-10-50-1B

+ Details

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

- Definition

Amount of gain (loss) on sale or disposal of assets utilized in financial service operations.

+ References

No definition available.

+ Details

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

- Definition

Cash received from sales of long-lived depreciable flight assets, including owned aircraft or capital improvements.

+ References

No definition available.

+ Details

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

- Details

Name:	us-gaap_PropertyPlantAndEquipmentByTypeAxis=us-gaap_FlightEquipmentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_IncomeStatementLocationAxis=us-gaap_NonoperatingIncomeExpenseMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DisposalGroupClassificationAxis=mei_DabirSurfacesBusinessMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DisposalGroupClassificationAxis=mei_DataMateBusinessMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_IncomeStatementLocationAxis=us-gaap_SellingGeneralAndAdministrativeExpensesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DisposalGroupClassificationAxis=us-gaap_DiscontinuedOperationsDisposedOfBySaleMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_MortgageLoansOnRealEstateDescriptionTypeOfPropertyAxis=srt_WarehouseMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Acquisition and Dispositions - Narrative (Details) - USD ($) $ in Millions			3 Months Ended		6 Months Ended	12 Months Ended
	Apr. 30, 2026	Jul. 14, 2025	May 02, 2026	Aug. 02, 2025	Oct. 28, 2023	May 02, 2026	May 03, 2025	Apr. 27, 2024	Oct. 13, 2023
Acquisitions and Dispositions [Line Items]
Gain loss on the sale of business, including transaction costs						$ 11.2	$ 0.0	$ 0.0
Aircraft
Acquisitions and Dispositions [Line Items]
Proceeds from sale of flight equipment								19.4
Other Expense (Income), Net \| Aircraft
Acquisitions and Dispositions [Line Items]
Gain on sale of aircraft								$ 2.4
Dabir Surfaces Business
Acquisitions and Dispositions [Line Items]
Consideration from sale of business									$ 1.5
Gain loss on the sale of business, including transaction costs					$ (0.6)
DataMate Business
Acquisitions and Dispositions [Line Items]
Consideration from sale of business			$ 16.4			16.4
DataMate Business \| Other Expense (Income), Net
Acquisitions and Dispositions [Line Items]
Gain loss on the sale of business, including transaction costs			11.2
DataMate Business \| Selling and Administrative Expenses
Acquisitions and Dispositions [Line Items]
Transaction costs						$ 1.4
Transaction
Acquisitions and Dispositions [Line Items]
Purchase price on purchase and sale agreement	$ 4.7
Gain on sale of assets			$ 1.0
Transaction \| Warehouse
Acquisitions and Dispositions [Line Items]
Purchase price on purchase and sale agreement		$ 1.3
Gain on sale of assets				$ 0.5