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OTHER COMPREHENSIVE INCOME (LOSS) (Details)	6 Months Ended
	Mar. 31, 2026
Other Comprehensive Income (Loss) [Abstract]
Income tax expense benefit tax rate for available for sale investments	25.00%

X

- Definition

Percentage of income tax expense benefit tax rate for available for sale investments.

+ References

No definition available.

+ Details

Name:	mgyr_IncomeTaxExpenseBenefitTaxRateForAvailbleForSaleInvestments
Namespace Prefix:	mgyr_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

X

- References

No definition available.

+ Details

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