Earnings per Share - Reconciliation of Numerators and Denominators of Basic and Diluted Earnings Per Share (Details) - USD ($) $ / shares in Units, shares in Thousands, $ in Thousands	12 Months Ended
	Sep. 30, 2021	Sep. 30, 2020	Sep. 30, 2019
Numerator for basic and diluted earnings per share
Net income	$ 392,084	$ 236,411	$ 192,124
Denominator — share:
Basic weighted-average shares (in shares)	28,734	29,067	28,980
Effect of dilutive securities (in shares)	526	865	1,314
Diluted weighted-average shares (in shares)	29,260	29,932	30,294
Earnings per share:
Basic earnings per share (in dollars per share)	$ 13.65	$ 8.13	$ 6.63
Diluted earnings per share (in dollars per share)	$ 13.40	$ 7.90	$ 6.34