Condensed Consolidated Statements of Changes in Stockholders' Equity (Unaudited) - USD ($) $ in Thousands	Open Market Repurchases [Member] Common Stock Outstanding [Member]	Open Market Repurchases [Member] Additional Paid-in Capital [Member]	Open Market Repurchases [Member] AOCI Attributable to Parent [Member]	Open Market Repurchases [Member] Retained Earnings [Member]	Open Market Repurchases [Member] Treasury Stock, Common [Member]	Open Market Repurchases [Member]	Accelerated Share Repurchases [Member] Common Stock Outstanding [Member]	Accelerated Share Repurchases [Member] Additional Paid-in Capital [Member]	Accelerated Share Repurchases [Member] AOCI Attributable to Parent [Member]	Accelerated Share Repurchases [Member] Retained Earnings [Member]	Accelerated Share Repurchases [Member] Treasury Stock, Common [Member]	Accelerated Share Repurchases [Member]	Common Stock Outstanding [Member]	Additional Paid-in Capital [Member]	AOCI Attributable to Parent [Member]	Retained Earnings [Member]	Treasury Stock, Common [Member]	Total
Balance (in shares) at Sep. 30, 2022													88,482,125
Balance at Sep. 30, 2022													$ 885	$ 1,992,017	$ (83,916)	$ 1,655,356	$ (200,956)	$ 3,363,386
Shares issued under restricted stock and purchase plans, net of shares withheld for employee taxes (in shares)													219,424
Shares issued under restricted stock and purchase plans, net of shares withheld for employee taxes													$ 2	(3,074)	0	0	0	(3,072)
Shares repurchases (in shares)							(10,072,055)						(3,972,634)
Shares repurchases								$ 0	$ 0	$ 0	$ (501,637)	$ (501,637)	$ 0	0	0	0	(174,322)	(174,322)
Retirement of treasury shares													(140)	(675,819)	0	0	675,959	0
Stock-based compensation													0	10,091	0	0	0	10,091
Net loss													0	0	0	(17,632)	0	(17,632)
Net investment hedge currency translation adjustment, net of tax													0	0	(70,478)	0	0	(70,478)
Foreign currency translation adjustments													0	0	113,140	0	0	113,140
Changes in unrealized gains on marketable securities, net of tax													0	0	4,109	0	0	4,109
Actuarial loss on pension plans, net of tax effects of $3 and $7 during the three and nine months ended June 30, 2024, respectively, and $0 during each of the three and nine months ended June 30, 2023																		0
Actuarial loss on pension plans, net of tax																		0
Other													$ 0	0	0	(85)	0	(85)
Balance (in shares) at Jun. 30, 2023													74,656,860
Balance at Jun. 30, 2023													$ 747	1,323,215	(37,145)	1,637,639	(200,956)	2,723,500
Balance (in shares) at Mar. 31, 2023													82,602,702
Balance at Mar. 31, 2023													$ 826	1,495,118	(38,870)	1,639,109	(200,956)	2,895,227
Shares issued under restricted stock and purchase plans, net of shares withheld for employee taxes (in shares)													8,713
Shares issued under restricted stock and purchase plans, net of shares withheld for employee taxes													$ 0	(18)	0	0	0	(18)
Shares repurchases (in shares)	(3,972,634)						(3,981,921)
Shares repurchases							$ 0	$ 0	$ 0	$ 0	$ (1,637)	$ (1,637)	0	0	0	0	(174,322)	(174,322)
Retirement of treasury shares													(80)	(175,880)	0	0	175,959	0
Stock-based compensation													0	3,995	0	0	0	3,995
Net loss													0	0	0	(1,470)	0	(1,470)
Net investment hedge currency translation adjustment, net of tax													0	0	(218)	0	0	(218)
Foreign currency translation adjustments													0	0	1,876	0	0	1,876
Changes in unrealized gains on marketable securities, net of tax													$ 0	0	67	0	0	67
Actuarial loss on pension plans, net of tax effects of $3 and $7 during the three and nine months ended June 30, 2024, respectively, and $0 during each of the three and nine months ended June 30, 2023																		0
Actuarial loss on pension plans, net of tax																		0
Balance (in shares) at Jun. 30, 2023													74,656,860
Balance at Jun. 30, 2023													$ 747	1,323,215	(37,145)	1,637,639	(200,956)	2,723,500
Balance (in shares) at Sep. 30, 2023													71,294,247
Balance at Sep. 30, 2023													$ 713	1,156,160	(62,426)	1,641,009	(200,956)	2,534,500
Shares issued under restricted stock and purchase plans, net of shares withheld for employee taxes (in shares)													224,802
Shares issued under restricted stock and purchase plans, net of shares withheld for employee taxes													$ 3	1,675	0	0	0	1,678
Shares repurchases (in shares)	(7,662,109)
Shares repurchases	$ (54)	$ 0	$ 0	$ 0	$ (416,693)	$ (416,747)
Retirement of treasury shares													(23)	(412,188)	0	0	412,211	0
Stock-based compensation													0	12,622	0	0	0	12,622
Net loss													0	0	0	(159,186)	0	(159,186)
Net investment hedge currency translation adjustment, net of tax													0	0	(7,971)	0	0	(7,971)
Foreign currency translation adjustments													0	0	21,725	0	0	21,725
Changes in unrealized gains on marketable securities, net of tax													0	0	3,799	0	0	3,799
Actuarial loss on pension plans, net of tax effects of $3 and $7 during the three and nine months ended June 30, 2024, respectively, and $0 during each of the three and nine months ended June 30, 2023													0	0	(22)	0	0	(22)
Actuarial loss on pension plans, net of tax													$ 0	0	(22)	0	0	(22)
Balance (in shares) at Jun. 30, 2024													63,856,940
Balance at Jun. 30, 2024													$ 639	758,269	(44,895)	1,481,823	(205,438)	1,990,398
Balance (in shares) at Mar. 31, 2024													68,075,910
Balance at Mar. 31, 2024													$ 681	999,333	(41,728)	1,488,405	(223,820)	2,222,871
Shares issued under restricted stock and purchase plans, net of shares withheld for employee taxes (in shares)													6,855
Shares issued under restricted stock and purchase plans, net of shares withheld for employee taxes													$ 0	1,678	0	0	0	1,678
Shares repurchases (in shares)	(4,225,825)
Shares repurchases	$ (42)	$ 0	$ 0	$ 0	$ (228,178)	$ (228,220)
Retirement of treasury shares													0	(246,560)	0	0	246,560	0
Stock-based compensation													0	3,818	0	0	0	3,818
Net loss													0	0	0	(6,582)	0	(6,582)
Net investment hedge currency translation adjustment, net of tax													0	0	317	0	0	317
Foreign currency translation adjustments													0	0	(4,000)	0	0	(4,000)
Changes in unrealized gains on marketable securities, net of tax													0	0	523	0	0	523
Actuarial loss on pension plans, net of tax effects of $3 and $7 during the three and nine months ended June 30, 2024, respectively, and $0 during each of the three and nine months ended June 30, 2023													0	0	(7)	0	0	(7)
Actuarial loss on pension plans, net of tax													$ 0	0	(7)	0	0	(7)
Balance (in shares) at Jun. 30, 2024													63,856,940
Balance at Jun. 30, 2024													$ 639	$ 758,269	$ (44,895)	$ 1,481,823	$ (205,438)	$ 1,990,398