DEBT - Credit Facilities (Details) $ in Millions	12 Months Ended
Sep. 30, 2024 USD ($) item
Revolving credit facility
Number of credit facility agreements \| item	3
Cross default provisions	$ 0.0
Facilities
Revolving credit facility
Borrowing capacity	300.0
Maximum credit advances for certain inventory purchases under the facilities	30.0
Credit limit	212.4
Outstanding borrowings	121.3
Credit available	$ 91.1
Average interest rate	6.82%
Peak borrowings	$ 181.8
Average borrowings	134.5
Average availability	$ 81.0

Cumulative provision for cross default accumulated on the balance sheet.

No definition available.

Name:	dit_CrossDefaultProvisions
Namespace Prefix:	dit_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Average borrowing capacity under the credit facility during the period.

+ References

No definition available.

+ Details

Name:	dit_LineOfCreditFacilityAverageBorrowingCapacity
Namespace Prefix:	dit_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Maximum credit advances for certain inventory purchases under the facilities.

+ References

No definition available.

+ Details

Name:	dit_LineOfCreditFacilityMaximumCreditAdvancesForCertainInventoryPurchases
Namespace Prefix:	dit_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Number of credit facilities agreement entered.

+ References

No definition available.

+ Details

Name:	dit_NumberOfCreditFacilitiesAgreements
Namespace Prefix:	dit_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	instant

- Definition

The carrying value as of the balance sheet date of the current and noncurrent portions of long-term obligations drawn from a line of credit, which is a bank's commitment to make loans up to a specific amount. Examples of items that might be included in the application of this element may consist of letters of credit, standby letters of credit, and revolving credit arrangements, under which borrowings can be made up to a maximum amount as of any point in time conditional on satisfaction of specified terms before, as of and after the date of drawdowns on the line. Includes short-term obligations that would normally be classified as current liabilities but for which (a) postbalance sheet date issuance of a long term obligation to refinance the short term obligation on a long term basis, or (b) the enterprise has entered into a financing agreement that clearly permits the enterprise to refinance the short-term obligation on a long term basis and the following conditions are met (1) the agreement does not expire within 1 year and is not cancelable by the lender except for violation of an objectively determinable provision, (2) no violation exists at the BS date, and (3) the lender has entered into the financing agreement is expected to be financially capable of honoring the agreement.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(22))
-SubTopic 10
-Topic 210
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480566/210-10-S99-1

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 944
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03(a)(16)(a)(2))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479440/944-210-S99-1

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 942
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(16))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479853/942-210-S99-1

+ Details

Name:	us-gaap_LineOfCredit
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Average amount borrowed under the credit facility during the period.

+ References

No definition available.

+ Details

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

- Definition

Amount of current borrowing capacity under the credit facility considering any current restrictions on the amount that could be borrowed (for example, borrowings may be limited by the amount of current assets), but without considering any amounts currently outstanding under the facility.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.19(b),22(b))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480566/210-10-S99-1

+ Details

Name:	us-gaap_LineOfCreditFacilityCurrentBorrowingCapacity
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

The effective interest rate during the reporting period.

+ References

+ Details

Name:	us-gaap_LineOfCreditFacilityInterestRateDuringPeriod
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
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 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.4-08(f))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480678/235-10-S99-1

+ Details

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

- Definition

Maximum amount borrowed under the credit facility at any time during the period.

+ References

No definition available.

+ Details

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

- Definition

Maximum borrowing capacity under the credit facility without consideration of any current restrictions on the amount that could be borrowed or the amounts currently outstanding under the facility.

+ References

+ Details

Name:	us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of borrowing capacity currently available under the credit facility (current borrowing capacity less the amount of borrowings outstanding).

+ References

+ Details

Name:	us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Details

Name:	us-gaap_CreditFacilityAxis=dit_FacilitiesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: