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401(K) EMPLOYEE CONTRIBUTION PLAN (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 30, 2025	Sep. 30, 2024
401(K) Employee Contribution Plan [Abstract]
Contributed amount	$ 278	$ 255

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- References

No definition available.

+ Details

Name:	mgyr_KEmployeeContributionPlanAbstract
Namespace Prefix:	mgyr_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

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- Definition

Amount of contributions made by employer into fund established for purposes of making future disbursement to individual in accordance with deferred compensation arrangement.

+ References

No definition available.

+ Details

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