Debt - Schedule of Aggregate Annual Maturities of Long-Term Debt (Details) $ in Thousands	Sep. 30, 2025 USD ($)
Line of Credit Facility [Line Items]
2026	$ 2,815
2027	11,318
2028	10,577
2029	15,000
2030	264,595
Total	304,305
2025 Credit Facility Revolver
Line of Credit Facility [Line Items]
2026	0
2027	0
2028	0
2029	0
2030	107,095
Total	107,095
2025 Credit Facility Term Loan
Line of Credit Facility [Line Items]
2026	2,500
2027	10,000
2028	10,000
2029	10,000
2030	157,500
Total	190,000
Aircraft Loan
Line of Credit Facility [Line Items]
2026	315
2027	1,318
2028	577
2029	5,000
2030	0
Total	$ 7,210

Long term debt maturities noncurrent repayments net.

No definition available.

Name:	meg_LongTermDebtMaturitiesNoncurrentRepaymentsNet
Namespace Prefix:	meg_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Long term debt non current maturities repayment last six months in next fiscal year.

+ References

No definition available.

+ Details

Name:	meg_LongTermDebtNonCurrentMaturitiesRepaymentLastSixMonthsInNextFiscalYear
Namespace Prefix:	meg_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- 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/2009/role/commonPracticeRef
-Topic 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S50
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480738/235-10-S50-1

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.4-08(f))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480678/235-10-S99-1

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 6
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481544/470-10-50-6

Reference 4: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 470
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 6
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481544/470-10-50-6

+ Details

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

- Definition

Amount of long-term debt payable, sinking fund requirement, and other securities issued that are redeemable by holder at fixed or determinable price and date, maturing in fifth fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 942
-SubTopic 235
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477314/942-235-S99-2

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S50
-Paragraph 4
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480738/235-10-S50-4

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 3
-Subparagraph (SX 210.12-04(a))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480678/235-10-S99-3

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1E
-Subparagraph (d)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1E

Reference 5: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-SubTopic 10
-Topic 470
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481544/470-10-50-1

+ Details

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

- Definition

Amount of long-term debt payable, sinking fund requirement, and other securities issued that are redeemable by holder at fixed or determinable price and date, maturing in fourth fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Amount of long-term debt payable, sinking fund requirement, and other securities issued that are redeemable by holder at fixed or determinable price and date, maturing in third fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Amount of long-term debt payable, sinking fund requirement, and other securities issued that are redeemable by holder at fixed or determinable price and date, maturing in second fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Details

Name:	us-gaap_CreditFacilityAxis=meg_TwentyTwentyFiveRevolvingCreditFacilityMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=meg_TwentyTwentyFiveCreditFacilityTermLoanMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=meg_AircraftLoanMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: