Consolidated Statements of Stockholders' Equity - USD ($) $ in Thousands	Total	Class A	Class B	Common Stock Class A	Common Stock Class B	Treasury Stock	Additional Paid-In Capital	Retained Earnings (Accumulated Deficit)	Accumulated Other Comprehensive Income (Loss)
Beginning balance (in shares) at Sep. 30, 2021				154,866,313	100
Beginning balance at Sep. 30, 2021	$ 1,421,495			$ 155	$ 0	$ 0	$ 1,615,236	$ (193,896)	$ 0
Beginning balance, treasury stock (in shares) at Sep. 30, 2021						0
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	67,158							67,158
Other comprehensive income	0
Stock-based compensation	17,971						17,971
Exercise of vested stock options (in shares)				260,649
Exercise of vested stock options	5,995						5,995
Cancellation of restricted stock awards (in shares)				(16,425)
Issuance of common stock under employee stock plan net of shares withheld for taxes (in shares)				46,683
Issuance of common stock under employee stock plan, net of shares withheld for taxes	(429)						(429)
Treasury stock purchases (in shares)						4,116,570
Treasury stock purchases	(81,483)					$ (73,088)	(8,395)
Ending balance (in shares) at Sep. 30, 2022				155,157,220	100
Ending balance at Sep. 30, 2022	1,430,707			$ 155	$ 0	$ (73,088)	1,630,378	(126,738)	0
Ending balance, treasury stock (in shares) at Sep. 30, 2022						4,116,570
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	62,361							62,361
Other comprehensive income	1,878								1,878
Stock-based compensation	18,518						18,518
Exercise of vested stock options (in shares)				650,138
Exercise of vested stock options	14,955			$ 1			14,954
Cancellation of restricted stock awards (in shares)				(19,306)
Issuance of common stock under employee stock plan net of shares withheld for taxes (in shares)				179,684
Issuance of common stock under employee stock plan, net of shares withheld for taxes	(1,528)						(1,528)
Treasury stock purchases (in shares)		4,152,000				4,151,853
Treasury stock purchases	(116,578)	$ (116,578)				$ (116,578)
Ending balance (in shares) at Sep. 30, 2023			100	155,967,736	100
Ending balance at Sep. 30, 2023	$ 1,410,313			$ 156	$ 0	$ (189,666)	1,662,322	(64,377)	1,878
Ending balance, treasury stock (in shares) at Sep. 30, 2023	8,268,423					8,268,423
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	$ 153,379							153,379
Other comprehensive income	(3,560)								(3,560)
Stock-based compensation	25,923						25,923
Exercise of vested stock options (in shares)				865,775
Exercise of vested stock options	20,853			$ 1			20,852
Issuance of common stock under employee stock plan net of shares withheld for taxes (in shares)				315,210
Issuance of common stock under employee stock plan, net of shares withheld for taxes	(5,214)						(5,214)
Conversion of Class B common stock into Class A common stock (in shares)				100	(100)
Treasury stock purchases (in shares)		5,866,000				5,866,135
Treasury stock purchases	(244,829)	$ (244,828)				$ (235,012)	(9,817)
Ending balance (in shares) at Sep. 30, 2024		143,014,263	0	157,148,821	0
Ending balance at Sep. 30, 2024	$ 1,356,865			$ 157	$ 0	$ (424,678)	$ 1,694,066	$ 89,002	$ (1,682)
Ending balance, treasury stock (in shares) at Sep. 30, 2024	14,134,558					14,134,558