Equity-based Compensation - Assumptions Used in Calculating Fair Value of Options (Parenthetical) (Detail) - USD ($) $ in Thousands	12 Months Ended
Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022
Share-Based Payment Arrangement [Abstract]
Share-Based Payment Arrangement, Expense, Tax Benefit	$ 21,169	$ 17,986	$ 15,066

Amount of tax benefit for recognition of expense of award under share-based payment arrangement.

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

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