General Description of the Plan - (Details) - EBP 002 - USD ($)	12 Months Ended
Dec. 31, 2025	Dec. 31, 2024
General Description of the Plan [Line Items]
Eligible compensation	80.00%
Discretionary matching contributions percentage	100.00%
Employees’ elective contributions	4.00%
Employer contributions	$ 268,413
Individual participant accounts	50.00%
Interest rates on loans percentage	4.25%	9.50%
Contribution vested percentage	100.00%
Vesting percentage	20.00%
Forfeited amounts to fund plan administration expenses	$ 12,445
Forfeited funds held by the plan, value	14,093	$ 8,921
Forfeitures amounted, value	$ 15,943
Vested accounts and assets, percentage	100.00%
Maximum
General Description of the Plan [Line Items]
Eligible compensation	6.00%
Discretionary matching contributions percentage	50.00%
Employees’ elective contributions	4.00%
Participant accounts, value	$ 50,000
Minimum
General Description of the Plan [Line Items]
Eligible compensation	2.00%
Participant accounts, value	$ 1,000

EBP Defined Contribution Plan Employer Matching Contribution Vesting Percentage.

No definition available.

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

- Definition

Percentage of Employee Benefit Plan Employer Elective Contributions Participant Compensation Matched.

+ References

No definition available.

+ Details

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

- Definition

Employee Benefit Plan, Plan Termination Vesting Percentage.

+ References

No definition available.

+ Details

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

- Definition

Employee Benefit Plan Vesting Percentage.

+ References

No definition available.

+ Details

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

- Definition

Amount of increase in net asset available for benefit from contribution transferred from another qualified plan or from individual retirement account of participant in employee stock purchase, saving, or similar plan (employee benefit plan (EBP)). Excludes contribution for participant transmitted by employer of participant in EBP.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 962
-SubTopic 325
-Name Accounting Standards Codification
-Section 55
-Paragraph 17
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478873/962-325-55-17

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 962
-SubTopic 205
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.6A-04(4)(a)(1))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477804/962-205-S99-1

Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 962
-SubTopic 205
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.6A-04(4)(b))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477804/962-205-S99-1

Reference 4: http://www.xbrl.org/2003/role/recommendedDisclosureRef
-Topic 962
-SubTopic 205
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.6A-05(a)(Schedule III))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477804/962-205-S99-1

Reference 5: http://www.xbrl.org/2003/role/recommendedDisclosureRef
-Topic 962
-SubTopic 325
-Name Accounting Standards Codification
-Section 50
-Paragraph 2B
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477783/962-325-50-2B

Reference 6: http://www.xbrl.org/2003/role/recommendedDisclosureRef
-Topic 962
-SubTopic 205
-Name Accounting Standards Codification
-Section 45
-Paragraph 7
-Subparagraph (d)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477063/962-205-45-7

+ Details

Name:	us-gaap-ebp_EmployeeBenefitPlanChangeInNetAssetAvailableForBenefitIncreaseForParticipantContributionRollover
Namespace Prefix:	us-gaap-ebp_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- 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 962
-SubTopic 205
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478416/962-205-50-1

+ Details

Name:	us-gaap-ebp_EmployeeBenefitPlanDescriptionOfPlanLineItems
Namespace Prefix:	us-gaap-ebp_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Percentage of employer matching contribution on eligible participant contribution to employee stock purchase, saving, or similar plan (employee benefit plan (EBP)).

+ References

+ Details

Name:	us-gaap-ebp_EmployeeBenefitPlanEmployerContributionMatchingPercentage
Namespace Prefix:	us-gaap-ebp_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Percentage of participant compensation eligible for employer matching contribution for participant in employee stock purchase, saving, or similar plan (employee benefit plan (EBP)).

+ References

+ Details

Name:	us-gaap-ebp_EmployeeBenefitPlanEmployerContributionParticipantCompensationMatchedPercentage
Namespace Prefix:	us-gaap-ebp_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount of plan asset, in forfeited nonvested account, no longer allocated to participant in employee stock purchase, saving, or similar plan (employee benefit plan (EBP)).

+ References

+ Details

Name:	us-gaap-ebp_EmployeeBenefitPlanForfeitedNonvestedAccount
Namespace Prefix:	us-gaap-ebp_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of decrease in forfeited nonvested account of employee stock purchase, saving, or similar plan (employee benefit plan (EBP)) from administrative expense.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 962
-SubTopic 205
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (j)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478416/962-205-50-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 962
-SubTopic 205
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.6A-04(5)(c))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477804/962-205-S99-1

+ Details

Name:	us-gaap-ebp_EmployeeBenefitPlanForfeitedNonvestedAccountDecreaseForAdministrativeExpense
Namespace Prefix:	us-gaap-ebp_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount of decrease in forfeited nonvested account of employee stock purchase, saving, or similar plan (employee benefit plan (EBP)) from employer contribution.

+ References

+ Details

Name:	us-gaap-ebp_EmployeeBenefitPlanForfeitedNonvestedAccountDecreaseForEmployerContribution
Namespace Prefix:	us-gaap-ebp_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount of maximum account balance that participant in employee stock purchase, saving, or similar plan (employee benefit plan (EBP)) can borrow.

+ References

+ Details

Name:	us-gaap-ebp_EmployeeBenefitPlanNoteReceivableFromParticipantAccountMaximumBorrowingAmount
Namespace Prefix:	us-gaap-ebp_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Percentage of maximum account balance that participant in employee stock purchase, saving, or similar plan (employee benefit plan (EBP)) can borrow to total participant account balance.

+ References

+ Details

Name:	us-gaap-ebp_EmployeeBenefitPlanNoteReceivableFromParticipantAccountMaximumBorrowingToTotalAccountPercentage
Namespace Prefix:	us-gaap-ebp_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

Interest rate on participant loan in schedule of asset held for investment of employee stock purchase, saving, or similar plan (employee benefit plan (EBP)).

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Name Employee Retirement Income Security Act of 1974
-Number 2520
-Section 103
-Subsection 10
-Paragraph b
-Subparagraph (1)(i)(D)
-Publisher DOL-EBSA

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 962
-SubTopic 205
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.6A-05(a)(Schedule I))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477804/962-205-S99-1

+ Details

Name:	us-gaap-ebp_EmployeeBenefitPlanParticipantLoanInterestRate
Namespace Prefix:	us-gaap-ebp_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Details

Name:	dei_LegalEntityAxis=mgyr_EBP002Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_RangeAxis=srt_MaximumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_RangeAxis=srt_MinimumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: