Share-Based Compensation - Restricted Stock Plan (Details) - USD ($) $ / shares in Units, $ in Millions	12 Months Ended
Sep. 30, 2023	Sep. 30, 2022
Number of Shares Outstanding
Number of shares outstanding, beginning (in shares)	579,666
Number of shares outstanding, granted (in shares)	413,545
Number of shares outstanding, vested (in shares)	(305,561)
Number of shares outstanding, forfeited (in shares)	(638)
Number of shares outstanding, ending (in shares)	687,012	579,666
Weighted Average Grant Date Fair Value
Weighted average grant date fair value, beginning (in dollar per share)	$ 60.22
Weighted average grant date fair value, granted (in dollar per share)	93.59
Weighted average grant date fair value, vested (in dollar per share)	58.38
Weighted average grant date fair value, forfeited (in dollar per share)	80.69
Weighted average grant date fair value, ending (in dollars per share)	$ 81.10	$ 60.22
Stock Option Activity, Additional Disclosures
Weighted average remaining term (in years)	1 year 2 months 26 days	1 year 2 months 19 days
Aggregate intrinsic value	$ 66.5	$ 48.1

No definition available.

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- Definition

The number of equity-based payment instruments, excluding stock (or unit) options, that were forfeited during the reporting period.

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Weighted average fair value as of the grant date of equity-based award plans other than stock (unit) option plans that were not exercised or put into effect as a result of the occurrence of a terminating event.

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The number of grants made during the period on other than stock (or unit) option plans (for example, phantom stock or unit plan, stock or unit appreciation rights plan, performance target plan).

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- Definition

The weighted average fair value at grant date for nonvested equity-based awards issued during the period on other than stock (or unit) option plans (for example, phantom stock or unit plan, stock or unit appreciation rights plan, performance target plan).

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- Definition

The number of non-vested equity-based payment instruments, excluding stock (or unit) options, that validly exist and are outstanding as of the balance sheet date.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)(2)(i)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480429/718-10-50-2

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)(2)(ii)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480429/718-10-50-2

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- Definition

A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

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No definition available.

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- Definition

Per share or unit weighted-average fair value of nonvested award under share-based payment arrangement. Excludes share and unit options.

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- Definition

Weighted average remaining contractual term for equity-based awards excluding options, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 718
-SubTopic 10
-Subparagraph (e)(1)
-Name Accounting Standards Codification
-Paragraph 2
-Section 50
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480429/718-10-50-2

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- Definition

The number of equity-based payment instruments, excluding stock (or unit) options, that vested during the reporting period.

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- Definition

The weighted average fair value as of grant date pertaining to an equity-based award plan other than a stock (or unit) option plan for which the grantee gained the right during the reporting period, by satisfying service and performance requirements, to receive or retain shares or units, other instruments, or cash in accordance with the terms of the arrangement.

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- Definition

Intrinsic value of outstanding award under share-based payment arrangement. Excludes share and unit options.

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No definition available.

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