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Stockholders' Equity (Narrative) (Details) - USD ($) $ / shares in Units, $ in Thousands |  |  |  | 1 Months Ended | 12 Months Ended |
--- | --- | --- | --- | --- | --- | ---
Jan. 31, 2024 | Nov. 01, 2023 | Jan. 31, 2022 | Nov. 30, 2019 | Sep. 30, 2024 | Sep. 30, 2023 | Sep. 30, 2022 | Jan. 22, 2022
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |  |  |
Total unrecognized compensation cost related to non-vested stock-based compensation arrangements |  |  |  |  | $ 26,694 |  |  |
Forfeiture rate, Board of Directors |  |  |  |  | 0.00% |  |  |
Forfeiture rate, non-Board of Directors |  |  |  |  | 7.40% |  |  |
Stock-based compensation expense, before tax |  |  |  |  | $ 33,052 | $ 23,958 | $ 20,109 |
Unrecognized compensation cost is expected to be recognized over a weighted-average period |  |  |  |  | 1 year 9 months 14 days |  |  |
Executive Separation and Release Agreement [Member] |  |  |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |  |  |
Stock-based compensation expense, before tax |  |  |  |  | $ 1,682 | $ 1,265 |  |
Restricted Stock Units (RSUs) [Member] | RSU Agreement prior to November 14, 2023 [Member] |  |  |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |  |  |
Vesting period, in years |  |  |  |  | 4 years |  |  |
Vesting rate |  |  |  |  | 25.00% |  |  |
Restricted Stock Units (RSUs) [Member] | RSUs Granted after November 14, 2023 [Member] |  |  |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |  |  |
Vesting period, in years |  |  |  |  | 3 years |  |  |
Vesting rate |  |  |  |  | 33.30% |  |  |
Stock Options [Member] |  |  |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |  |  |
Vesting period, in years |  |  |  |  | 4 years |  |  |
Vested contractual term, in years |  |  |  |  | 10 years |  |  |
Exercise prices of stock options outstanding |  |  |  |  | $ 86.03 | $ 80.48 |  |
Weighted-average exercise price |  |  |  |  | $ 137.36 |  |  |
Stock Options [Member] | RSU Agreement prior to November 14, 2023 [Member] |  |  |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |  |  |
Vesting rate |  |  |  |  | 25.00% |  |  |
Performance Restricted Stock Units [Member] |  |  |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |  |  |
Award performance period (in years) |  | 3 years |  |  |  |  |  |
Performance based criteria plan payout percentage, target |  | 100.00% |  |  |  |  |  |
Discount for dividends |  |  |  |  | 0.00% |  |  |
Performance Restricted Stock Units [Member] | Maximum [Member] |  |  |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |  |  |
Performance based criteria plan payout percentage |  | 150.00% |  |  |  |  |  |
Performance Restricted Stock Units [Member] | Minimum [Member] |  |  |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |  |  |
Performance based criteria plan payout percentage |  | 0.00% |  |  |  |  |  |
2019 Authorization [Member] |  |  |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |  |  |
Stock repurchase program authorized amount |  |  |  |  |  |  | $ 26,742 |
Repurchase period in years |  |  |  | 3 years |  |  |  |
Stock repurchase program, number of shares authorized to be repurchased |  |  |  |  |  |  | 233,000 |
2019 Authorization [Member] | Maximum [Member] |  |  |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |  |  |
Stock repurchase program authorized amount |  |  |  | $ 500,000 |  |  |  |
2022 Authorization [Member] | Maximum [Member] |  |  |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |  |  |
Stock repurchase program authorized amount |  |  |  |  |  |  |  | $ 800,000
2022 Authorization [Member] |  |  |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |  |  |
Stock repurchase program authorized amount |  |  |  |  |  | $ 126,380 | $ 446,042 |
Repurchase period in years |  |  | 2 years |  |  |  |  |
Stock repurchase program, number of shares authorized to be repurchased |  |  |  |  |  | 1,060,000 | 3,890,000 |
2024 Authorization [Member] |  |  |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |  |  |
Stock repurchase program authorized amount | $ 600,000 |  |  |  | $ 390,819 |  |  |
Repurchase period in years | 3 years |  |  |  |  |  |  |
Stock repurchase program, number of shares authorized to be repurchased |  |  |  |  | 2,236,000 |  |  |

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