Equity-based Compensation - Additional Information (Detail) - USD ($) $ / shares in Units, $ in Thousands	12 Months Ended
	Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022	Jan. 31, 2024	Feb. 13, 2023	Nov. 08, 2022
Awards granted under the Equity Incentive Plan
Maximum number of shares authorized to be granted				70,550
Unrecognized compensation expense	$ 80,539
Employee Share Purchase Plan [Member]
Awards granted under the Equity Incentive Plan
Maximum number of shares authorized to be granted					2,400,000	2,400,000
Number of shares authorized under the employee share purchase plan	548,000
Stock option awards, term	10 years
Total intrinsic value of options exercised	$ 10,899	$ 24,721	$ 33,096
Aggregate intrinsic value of stock options outstanding	27,291
Aggregate intrinsic value of stock options exercisable	27,049
Unrecognized compensation expense	$ 1,417
Employee share purchase plan, Share	548,000	0
Purchase price per ordinary share	$ 68.95
Share based compensation discount from purchased market price offering rate	85.00%
Restricted Stock [Member]
Awards granted under the Equity Incentive Plan
Value of restricted shares vested	$ 72,404	$ 60,646	40,615
Restricted Stock Units (RSUs) [Member]
Awards granted under the Equity Incentive Plan
Value of restricted shares vested	$ 17,722	$ 13,125	$ 5,891
Minimum [Member]
Awards granted under the Equity Incentive Plan
Awards granted under the Equity Incentive Plan, vesting period	3 years
Maximum [Member]
Awards granted under the Equity Incentive Plan
Maximum number of shares authorized to be granted	73,550
Awards granted under the Equity Incentive Plan, vesting period	4 years
Maximum [Member] | Employee Share Purchase Plan [Member]
Awards granted under the Equity Incentive Plan
Share based compensation payment award maximum employee subscription rate	10.00%