Shareholders' Equity - Summary of Combined Stock Option Activity and Related Information for Stock Options Granted (Details) - Stock Options - 2010 Plan and 2007 Plan	9 Months Ended
Jan. 30, 2021 $ / shares shares
Share Based Compensation Arrangement By Share Based Payment Award Options Outstanding [Roll Forward]
Outstanding - beginning balance (in shares) \| shares	106,668
Exercised (in shares) \| shares	(5,000)
Cancelled (in shares) \| shares	(1,668)
Outstanding - ending balance (in shares) \| shares	100,000
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Weighted Average Exercise Price [Roll Forward]
Wtd. Avg. Exercise Price, Outstanding - beginning balance (in dollars per share) \| $ / shares	$ 35.76
Wtd. Avg. Exercise Price, Exercised (in dollars per share) \| $ / shares	10.55
Wtd. Avg. Exercise Price, Cancelled (in dollars per share) \| $ / shares	37.01
Wtd. Avg. Exercise Price, Outstanding - ending balance (in dollars per share) \| $ / shares	$ 37.01

The number of shares under options that were cancelled during the reporting period as a result of occurrence of a terminating event specified in contractual agreements pertaining to the stock option plan.

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Number of options outstanding, including both vested and non-vested options.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(1)(i)-(ii)
-URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

+ References

No definition available.

+ Details

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

- Definition

Weighted average price at which grantees can acquire the shares reserved for issuance under the stock option plan.

+ References

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice
Namespace Prefix:	us-gaap_
Data Type:	num:perShareItemType
Balance Type:	na
Period Type:	instant

- References

No definition available.

+ Details

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

- Definition

Weighted average price at which option holders acquired shares when converting their stock options into shares.

+ References

No definition available.

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice
Namespace Prefix:	us-gaap_
Data Type:	num:perShareItemType
Balance Type:	na
Period Type:	duration

- Definition

Weighted average price at which grantees could have acquired the underlying shares with respect to stock options that were terminated.

+ References

No definition available.

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice
Namespace Prefix:	us-gaap_
Data Type:	num:perShareItemType
Balance Type:	na
Period Type:	duration

- Definition

Number of share options (or share units) exercised during the current period.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(1)(iv)(2)
-URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 505
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.3-04)
-URI http://asc.fasb.org/extlink&oid=120397183&loc=d3e187085-122770

Reference 3: 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(28))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

Reference 4: 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(29))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

Reference 5: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 505
-SubTopic 10
-Section 50
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=109259400&loc=d3e21463-112644

+ Details

Name:	us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Details

Name:	us-gaap_AwardTypeAxis=us-gaap_EmployeeStockOptionMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_PlanNameAxis=mei_TwoThousandTenAndTwoThousandSevenStockPlanMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: