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, 2024	Sep. 30, 2023	Sep. 30, 2022
Numerator for basic and diluted earnings per share
Net income	$ 512,811	$ 429,375	$ 373,541
Denominator — share:
Basic weighted-average shares (in shares)	24,676	24,986	26,042
Effect of dilutive securities (in shares)	403	381	305
Diluted weighted-average shares (in shares)	25,079	25,367	26,347
Diluted earnings per share (in dollars per share)	$ 20.45	$ 16.93	$ 14.18
Basic earnings per share (in dollars per share)	$ 20.78	$ 17.18	$ 14.34