Share-Based Compensation - Options by Exercise Price (Details)	12 Months Ended
	Sep. 30, 2023 $ / shares shares
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]
Number of outstanding options (in shares) | shares	1,175,364
Weighted average exercise price (in dollars per share)	$ 53.46
Weighted average remaining term (in years)	3 years 9 months 18 days
$40.00 - $45.00
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]
Exercise price range, lower range limit (in dollars per share)	$ 40.00
Exercise price range, upper range limit (in dollars per share)	$ 45.00
Number of outstanding options (in shares) | shares	700,000
Weighted average exercise price (in dollars per share)	$ 45.00
Weighted average remaining term (in years)	3 years 2 months 4 days
$45.00 - $95.00
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]
Exercise price range, lower range limit (in dollars per share)	$ 45.00
Exercise price range, upper range limit (in dollars per share)	$ 95.00
Number of outstanding options (in shares) | shares	475,364
Weighted average exercise price (in dollars per share)	$ 65.92
Weighted average remaining term (in years)	4 years 8 months 15 days