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Share-Based Compensation - Schedule of Stock Option Activity (Details) - USD ($) $ / shares in Units, $ in Millions | 12 Months Ended
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Sep. 30, 2025 | Sep. 30, 2024 | Sep. 30, 2023
Number of Options Outstanding |  |  |
Number of options outstanding, beginning (in shares) | 4,591,552 |  |
Number of options outstanding, granted (in shares) | 533,127 |  |
Number of options outstanding, exercised (in shares) | (407,084) |  |
Number of options outstanding, forfeited (in shares) | (55,993) |  |
Number of options outstanding, expired (in shares) | (851) |  |
Number of options outstanding, ending (in shares) | 4,660,751 | 4,591,552 |
Number of options outstanding, exercisable (in shares) | 1,234,595 |  |
Weighted Average Exercise Price |  |  |
Weighted average exercise price, beginning (in dollar per share) | $ 34.42 |  |
Weighted average exercise price, granted (in dollar per share) | 77.18 |  |
Weighted average exercise price, exercised (in dollar per share) | 26.26 |  |
Weighted average exercise price, forfeited (in dollar per share) | 39.62 |  |
Weighted average exercise price, expired (in dollar per share) | 27.60 |  |
Weighted average exercise price, ending (in dollar per share) | 39.97 | $ 34.42 |
Weighted average exercise price, exercisable (in dollar per share) | 23.47 |  |
Weighted Average Grant Date Fair Value |  |  |
Weighted average grant date fair value, beginning (in dollar per share) | 12.86 |  |
Weighted average grant date fair value, granted (in dollar per share) | 27.93 | 26.77 | $ 22.14
Weighted average grant date fair value, exercised (in dollar per share) | 8.43 |  |
Weighted average grant date fair value, forfeited (in dollar per share) | 13.39 |  |
Weighted average grant date fair value, expired (in dollar per share) | 10.84 |  |
Weighted average grant date fair value, ending (in dollar per share) | 14.96 | $ 12.86 |
Weighted average grant date fair value, exercisable (in dollar per share) | $ 6.83 |  |
Stock Option Activity, Additional Disclosures |  |  |
Weighted average remaining term | 4 years 5 months 19 days | 5 years 21 days |
Weighted average remaining term, exercisable | 1 year 9 months 14 days |  |
Aggregate intrinsic value | $ 284.1 | $ 88.7 |
Aggregate intrinsic value, exercisable | $ 95.6 |  |

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- Definition The weighted average grant-date fair value of options exercised during the reporting period as calculated by applying the disclosed option pricing methodology. + References No definition available. + Details
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- Definition The weighted average grant-date fair value of options expired during the reporting period as calculated by applying the disclosed option pricing methodology. + References No definition available. + Details
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- Definition The weighted average grant-date fair value of options forfeited during the reporting period as calculated by applying the disclosed option pricing methodology. + References No definition available. + Details
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- Definition The weighted average grant-date fair value of options outstanding as calculated by applying the disclosed option pricing methodology. + References No definition available. + Details
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- Definition Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Weighted Average Grant Date Fair Value [Roll Forward] + References No definition available. + Details
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- Definition The number of shares into which fully or partially vested stock options outstanding as of the balance sheet date can be currently converted under the option plan. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (c)(1)(iii) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480429/718-10-50-2 + Details
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- Definition The weighted-average price as of the balance sheet date at which grantees can acquire the shares reserved for issuance on vested portions of options outstanding and currently exercisable under the stock option plan. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (c)(1)(iii) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480429/718-10-50-2 + Details
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- Definition Number of options or other stock instruments for which the right to exercise has lapsed under the terms of the plan agreements. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (c)(1)(iv)(04) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480429/718-10-50-2 + Details
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- Definition The number of shares under options that were cancelled during the reporting period as a result of occurrence of a terminating event specified in contractual agreements pertaining to the stock option plan. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (c)(1)(iv)(03) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480429/718-10-50-2 + Details
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- Definition Gross number of share options (or share units) granted during the period. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (c)(1)(iv)(01) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480429/718-10-50-2 + Details
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- Definition The weighted average grant-date fair value of options granted during the reporting period as calculated by applying the disclosed option pricing methodology. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (d)(1) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480429/718-10-50-2 + Details
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- Definition The addition or reduction in the number of reserved shares that could potentially be issued under the option plan attributable to reasons other than grants, exercises, forfeitures, and expirations during the reporting period. + References Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (c)(1)(iv) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480429/718-10-50-2 + Details
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- Definition Amount by which the current fair value of the underlying stock exceeds the exercise price of options outstanding. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Name Accounting Standards Codification -Topic 718 -SubTopic 10 -Section 50 -Paragraph 2 -Publisher FASB -URI https://asc.fasb.org/1943274/2147480429/718-10-50-2 + Details
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- Definition Number of options outstanding, including both vested and non-vested options. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (c)(1)(i) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480429/718-10-50-2 Reference 2: http://www.xbrl.org/2003/role/disclosureRef -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (c)(1)(ii) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480429/718-10-50-2 + Details
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- Definition Weighted average price at which grantees can acquire the shares reserved for issuance under the stock option plan. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (c)(1)(i) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480429/718-10-50-2 Reference 2: http://www.xbrl.org/2003/role/disclosureRef -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (c)(1)(ii) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480429/718-10-50-2 + Details
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- Definition Weighted average price at which option holders acquired shares when converting their stock options into shares. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (c)(1)(iv)(02) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480429/718-10-50-2 + Details
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- Definition Weighted average price at which grantees could have acquired the underlying shares with respect to stock options of the plan that expired. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 718 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (c)(1)(iv)(04) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480429/718-10-50-2 + Details
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