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	3 Months Ended																12 Months Ended
	Sep. 30, 2019		Jun. 30, 2019		Mar. 31, 2019		Dec. 31, 2018		Sep. 30, 2018		Jun. 30, 2018		Mar. 31, 2018		Dec. 31, 2017		Sep. 30, 2019	Sep. 30, 2018	Sep. 30, 2017
Numerator for basic and diluted earnings per share
Net income	$ 54,584		$ 64,152		$ 33,381		$ 40,007		$ 32,713		$ 29,721		$ 31,169		$ 32,879		$ 192,124	$ 126,482	$ 133,414
Denominator — share:
Basic weighted-average shares (in shares)	28,918		28,967		29,074		28,961		29,077		29,708		29,985		30,078		28,980	29,711	30,862
Effect of dilutive securities (in shares)																	1,314	1,469	1,383
Diluted weighted-average shares (in shares)	30,290		30,292		30,259		30,336		30,702		31,161		31,300		31,561		30,294	31,180	32,245
Earnings per share:
Basic earnings per share (in dollars per share)	$ 1.89	[1]	$ 2.21	[1]	$ 1.15	[1]	$ 1.38	[1]	$ 1.13	[1]	$ 1.00	[1]	$ 1.04	[1]	$ 1.09	[1]	$ 6.63	$ 4.26	$ 4.32
Diluted earnings per share (in dollars per share)	$ 1.80	[1]	$ 2.12	[1]	$ 1.10	[1]	$ 1.32	[1]	$ 1.07	[1]	$ 0.95	[1]	$ 1.00	[1]	$ 1.04	[1]	$ 6.34	$ 4.06	$ 4.14

[1] Earnings per share is computed independently for each of the quarters presented. Therefore, the sum of the quarterly per share amounts may not equal the totals for the respective years.