Share-Based Compensation Plans - Stock Option Activity (Details) - USD ($) $ / shares in Units, $ in Thousands	12 Months Ended
Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2019
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding [Roll Forward]
Outstanding, beginning of period (in shares)	807,000
Granted (in shares)	113,000
Exercised (in shares)	(132,000)
Forfeited or canceled (in shares)	(9,000)
Outstanding, end of period (in shares)	779,000	807,000
Stock options, exercisable (in shares)	510,000
Stock options, expected to vest (in shares)	269,000
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Weighted Average Exercise Price [Abstract]
Outstanding, beginning of period (in dollars per share)	$ 75.87
Granted (in dollars per share)	147.67
Exercised (in dollars per share)	54.34
Forfeited or canceled (in dollars per share)	107.33
Outstanding, end of period (in dollars per share)	89.61	$ 75.87
Weighted average exercise price, exercisable (in dollars per share)	69.52
Weighted average exercise price, expected to vest (in dollars per share)	$ 127.60
Share-based Compensation Arrangement by Share-based Payment Award, Options, Additional Disclosures [Abstract]
Weighted average remaining contractual term, outstanding	6 years
Aggregate intrinsic value, outstanding	$ 29,654
Weighted average remaining contractual term, exercisable	4 years 10 months 24 days
Aggregate intrinsic value, exercisable	$ 27,763
Weighted average remaining contractual term, expected to vest	8 years 1 month 6 days
Aggregate intrinsic value, expected to vest	$ 1,891
Share-based Payment Arrangement
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Intrinsic value of options exercised	14,640	$ 19,077	$ 20,711
Cash received from exercise of options	7,190	9,350	13,193
Tax benefit from exercise of options	2,848	3,629	4,449
Fair value of options vested	$ 3,892	$ 3,765	$ 4,506

Amount of tax benefit from exercise of option under share-based payment arrangement.

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
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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.

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Weighted average price of options that were either forfeited or expired.

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Number of options outstanding, including both vested and non-vested options.

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Weighted average price at which grantees can acquire the shares reserved for issuance under the stock option plan.

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Amount by which current fair value of underlying stock exceeds exercise price of fully vested and expected to vest options outstanding. Includes, but is not limited to, unvested options for which requisite service period has not been rendered but that are expected to vest based on achievement of performance condition, if forfeitures are recognized when they occur.

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Number of fully vested and expected to vest options outstanding that can be converted into shares under option plan. Includes, but is not limited to, unvested options for which requisite service period has not been rendered but that are expected to vest based on achievement of performance condition, if forfeitures are recognized when they occur.

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Weighted average price at which option holders acquired shares when converting their stock options into shares.

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Weighted average remaining contractual term for vested portions of options outstanding and currently exercisable or convertible, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

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Weighted average remaining contractual term for fully vested and expected to vest options outstanding, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days. Includes, but is not limited to, unvested options for which requisite service period has not been rendered but that are expected to vest based on achievement of performance condition, if forfeitures are recognized when they occur.

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Number of share options (or share units) exercised during the current period.

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