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, 2022	Sep. 30, 2021	Sep. 30, 2020
Numerator for basic and diluted earnings per share
Net income	$ 373,541	$ 392,084	$ 236,411
Denominator — share:
Basic weighted-average shares (in shares)	26,042	28,734	29,067
Effect of dilutive securities (in shares)	305	526	865
Diluted weighted-average shares (in shares)	26,347	29,260	29,932
Earnings per share:
Basic earnings per share (in dollars per share)	$ 14.34	$ 13.65	$ 8.13
Diluted earnings per share (in dollars per share)	$ 14.18	$ 13.40	$ 7.90