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Stock-based compensation - Stock Option Grants, Vesting, and Exercises (Detail) - USD ($)
$ / shares in Units, $ in Millions
3 Months Ended
Dec. 31, 2021
Dec. 31, 2020
Disclosure Of Compensation Related Costs Sharebased Payments [Abstract]    
Weighted-average fair value per share of stock options granted   $ 15.62
Total grant date fair value of stock options vested $ 3.7 $ 4.1
Total intrinsic value of stock options exercised $ 4.1 $ 2.6