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COMMITMENTS (Schedule of Balance Sheet Information Related to Leases) (Details) - USD ($) $ in Thousands	Sep. 30, 2022	Sep. 30, 2021
Commitments and Contingencies Disclosure [Abstract]
Operating lease right-of-use asset	$ 3,292	$ 3,894
Operating lease liabilities	$ 3,605	$ 4,254
Weighted average remaining lease term in years	7 years	7 years 8 months 12 days
Weighted average discount rate	2.20%	2.20%

X

- Definition

Indicates line item in statement of financial position that includes operating lease liability.

+ References

No definition available.

+ Details

Name:	mgyr_OperatingLeaseLiabilityStatementsOfFinancialPositionExtensibleList
Namespace Prefix:	mgyr_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

X

- Definition

Indicates line item in statement of financial position that includes operating lease right-of-use asset.

+ References

No definition available.

+ Details

Name:	mgyr_OperatingLeaseRightOfUseAssetStatementsOfFinancialPositionExtensibleList
Namespace Prefix:	mgyr_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

X

- References

No definition available.

+ Details

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

X

- Definition

Weighted average discount rate for operating lease calculated at point in time.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 50
-Paragraph 4
-Subparagraph (g)(4)
-URI https://asc.fasb.org/extlink&oid=128292326&loc=SL77918686-209980

Reference 2: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 55
-Paragraph 53
-URI https://asc.fasb.org/extlink&oid=123414884&loc=SL77918982-209971

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

X

- Definition

Weighted average remaining lease term for operating lease, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 55
-Paragraph 53
-URI https://asc.fasb.org/extlink&oid=123414884&loc=SL77918982-209971

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 50
-Paragraph 4
-Subparagraph (g)(3)
-URI https://asc.fasb.org/extlink&oid=128292326&loc=SL77918686-209980

+ Details

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Namespace Prefix:	us-gaap_
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Balance Type:	na
Period Type:	instant