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Equity-based Compensation - Assumptions Used in Calculating Fair Value of Options (Parenthetical) (Detail) - USD ($) | 12 Months Ended
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Sep. 30, 2023 | Sep. 30, 2022 | Sep. 30, 2021
Share-Based Payment Arrangement [Abstract] |  |  |
Share-Based Payment Arrangement, Expense, Tax Benefit | $ 17,986 | $ 15,066 | $ 8,479

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- Definition Amount of tax benefit for recognition of expense of award under share-based payment arrangement. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (h)(1)(i) -Publisher FASB -URI https://asc.fasb.org//1943274/2147480429/718-10-50-2 + Details
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