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SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES - Selling, general and administrative, research and development expense (Details) - USD ($)	6 Months Ended
	Mar. 31, 2025	Mar. 31, 2024	Mar. 31, 2023
SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES
Selling expense	$ 451,145	$ 229,092	$ 445,154
General and administrative expense	3,770,496	1,396,655	1,366,888
Research and development expense	528,099	467,363	272,073
Total	$ 4,749,740	$ 2,093,110	$ 2,084,115

X

- Definition

It represents the value of selling, general and administrative, research and development expenses.

+ References

No definition available.

+ Details

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Namespace Prefix:	bgm_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

X

- References

No definition available.

+ Details

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

X

- Definition

The aggregate total of expenses of managing and administering the affairs of an entity, including affiliates of the reporting entity, which are not directly or indirectly associated with the manufacture, sale or creation of a product or product line.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 220
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Subparagraph (SX 210.5-03(4))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147483621/220-10-S99-2

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 220
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.6-07(2)(a))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479134/946-220-S99-1

+ Details

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Namespace Prefix:	us-gaap_
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Balance Type:	debit
Period Type:	duration

X

- Definition

Amount of expense for research and development. Includes, but is not limited to, cost for computer software product to be sold, leased, or otherwise marketed and writeoff of research and development assets acquired in transaction other than business combination or joint venture formation or both. Excludes write-down of intangible asset acquired in business combination or from joint venture formation or both, used in research and development activity.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 280
-SubTopic 10
-Name Accounting Standards Codification
-Section 55
-Paragraph 48
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482785/280-10-55-48

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 985
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481283/985-20-50-2

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 730
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482916/730-10-50-1

Reference 4: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 912
-SubTopic 730
-Name Accounting Standards Codification
-Section 25
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479532/912-730-25-1

+ Details

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Namespace Prefix:	us-gaap_
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Balance Type:	debit
Period Type:	duration

X

- Definition

Expenses recognized in the period that are directly related to the selling and distribution of products or services.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 220
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Subparagraph (SX 210.5-03(4))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147483621/220-10-S99-2

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration