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Equity-based Compensation - Assumptions Used in Calculating Fair Value of Options (Parenthetical) (Detail) - USD ($)
$ in Thousands
12 Months Ended
Sep. 30, 2025
Sep. 30, 2024
Sep. 30, 2023
Share-Based Payment Arrangement [Abstract]      
Share-Based Payment Arrangement, Expense, Tax Benefit $ 20,693 $ 21,169 $ 17,986