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Stock-based Compensation - Additional Information (Details) - USD ($) $ / shares in Units, $ in Millions | 12 Months Ended
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Sep. 30, 2025 | Sep. 30, 2024 | Sep. 30, 2023
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award, Award Vesting Period (Year) | 3 years |  |
Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Shares Authorized (in shares) | 1,500,000 |  |
Share-Based Compensation Arrangement by Share-Based Payment Award, Shares Deferred (in shares) | 79,815 |  |
Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Expected Dividend Rate | 0.00% | 0.00% | 0.00%
Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Amount | $ 8.7 |  |
Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Period for Recognition (Year) | 1 year 9 months 18 days |  |
Performance-contingent Restricted Share Units |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period (in shares) | 103,780 |  |
Granted, weighted average grant date fair value (in dollars per share) | $ 76.52 |  |
Performance-contingent Restricted Share Units | Executive Officers and Key Employees |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period (in shares) | 103,780 |  |
Granted, weighted average grant date fair value (in dollars per share) | $ 76.52 | $ 74.23 | $ 79.88
Share Based Compensation Arrangement By Share Based Payment Award, Maximum Target Award Percentage | 200.00% |  |
Share Based Compensation Arrangement By Share Based Payment Award, Number of Shares to Be Issued at Maximum Performance Target (in shares) | 564,862 |  |
Time-vested Restricted Stock |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period (in shares) | 57,030 |  |
Granted, weighted average grant date fair value (in dollars per share) | $ 72 |  |
Time-vested Restricted Stock | Executive Officers and Key Employees |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period (in shares) | 57,030 |  |
Granted, weighted average grant date fair value (in dollars per share) | $ 72 | 60.68 | 71.91
Time-vested Restricted Stock | Non Employee Directors |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period (in shares) | 15,750 |  |
Granted, weighted average grant date fair value (in dollars per share) | $ 71.38 | $ 58.03 | $ 75.59
Performance-contingent Restricted Stock Unit and Time-vested Restricted Stocks |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |
Share-Based Payment Arrangement, Shares Withheld for Tax Withholding Obligation (in shares) | 26,892 | 24,724 | 18,428
Share-Based Compensation Arrangement by Share-Based Payment Award, Shares Withheld for Tax Withholding Obligations, Weighted Average Price Per Share (in dollars per share) | $ 73.45 | $ 60.73 | $ 72.03
Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Vested in Period, Fair Value | $ 8.0 | $ 11.9 | $ 8.6
Share Based Compensation Tax Benefit Realized From Exercise Of Equity Instruments Other Than Stock Options | $ 4.0 | $ 3.7 | $ 3.2

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