CONSOLIDATED STATEMENTS OF STOCKHOLDERS' EQUITY - USD ($) shares in Thousands, $ in Thousands	Total	Cumulative effect of adoption of ASU 2020-06	Common Stock	Additional Paid-in Capital	Additional Paid-in Capital Cumulative effect of adoption of ASU 2020-06	Retained Earnings	Retained Earnings Cumulative effect of adoption of ASU 2020-06	Accumulated Other Comprehensive Loss
Beginning balance (in shares) at Sep. 30, 2021			56,057
Beginning balance at Sep. 30, 2021	$ 672,238	$ (36,638)	$ 560	$ 403,312	$ (62,804)	$ 326,781	$ 26,166	$ (58,415)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Stock compensation	5,053			5,053
Transfer of consideration for other investment (in shares)			213
Transfer of consideration for other investment	1,500		$ 2	1,498
Release of restricted stock, net of shares withheld for taxes (in shares)			393
Release of restricted stock, net of shares withheld for taxes	4		$ 4
Taxes paid related to net share settlement of equity awards	(792)			(792)
Foreign currency translation gain (loss)	2,746					0		2,746
Purchase and retirement of treasury stock (in shares)			(238)
Purchase and retirement of treasury stock	(2,040)		$ (2)	(937)		(1,101)
Net income	50,160					50,160
Ending balance (in shares) at Sep. 30, 2022			56,425
Ending balance at Sep. 30, 2022	692,231		$ 564	345,330		402,006		(55,669)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Stock compensation	9,539			9,539
Transfer of equity consideration for acquisition (in shares)			10
Transfer of equity consideration for acquisition	99		$ 0	99
Release of restricted stock, net of shares withheld for taxes (in shares)			373
Release of restricted stock, net of shares withheld for taxes	5		$ 5
Taxes paid related to net share settlement of equity awards (in shares)			(1)
Taxes paid related to net share settlement of equity awards	(1,148)			(1,148)
Foreign currency translation gain (loss)	23,567							23,567
Purchase and retirement of treasury stock (in shares)			(1,967)
Purchase and retirement of treasury stock	(16,988)		$ (20)	(7,639)		(9,329)
Net income	38,463					38,463
Ending balance (in shares) at Sep. 30, 2023			54,840
Ending balance at Sep. 30, 2023	745,768		$ 549	346,181		431,140		(32,102)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Stock compensation	10,406			10,406
Release of restricted stock, net of shares withheld for taxes (in shares)			855
Release of restricted stock, net of shares withheld for taxes	49		$ 9	40
Settlement of conversion premium of convertible notes due 2024 (in shares)			77
Settlement of conversion premium of convertible notes due 2024	0		$ 1	(1)
Taxes paid related to net share settlement of equity awards (in shares)			0
Taxes paid related to net share settlement of equity awards	(3,294)			(3,294)
Foreign currency translation gain (loss)	(19,445)							(19,445)
Purchase and retirement of treasury stock (in shares)			(1,219)
Purchase and retirement of treasury stock	(12,008)		$ (13)	(4,966)		(7,029)
Net income	83,095					83,095
Ending balance (in shares) at Sep. 30, 2024			54,553
Ending balance at Sep. 30, 2024	$ 804,571		$ 546	$ 348,366		$ 507,206		$ (51,547)