Consolidated Statements of Changes in Stockholders' Equity - Unaudited - USD ($) $ in Thousands	Total	Common Stock	Additional Paid-in Capital	Treasury Stock	Retained Earnings	Accumulated Other Comprehensive Loss
Balance, beginning of period (in shares) at Aug. 31, 2021		41,163,192
Beginning balance at Aug. 31, 2021	$ 1,016,353	$ 412	$ 1,048,305	$ (905,917)	$ 912,515	$ (38,962)
Beginning balance, treasury stock (in shares) at Aug. 31, 2021				3,547,773
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	217,585				217,585
Other comprehensive income (loss)	(16,886)					(16,886)
Common stock issued for employee stock plans (in shares)		303,709		260
Common stock issued for employee stock plans	56,799	$ 3	56,924	$ (128)
Vesting of restricted stock (in shares)		18,360		7,162
Vesting of restricted stock	$ (3,130)			$ (3,130)
Repurchase of common stock (in shares)	46,200			46,200
Repurchases of common stock	$ (18,639)			$ (18,639)
Stock-based compensation expense	25,937		25,937
Dividends declared	(62,038)				(62,038)
Balance, end of period (in shares) at Feb. 28, 2022		41,485,261
Ending balance at Feb. 28, 2022	1,215,981	$ 415	1,131,166	$ (927,814)	1,068,062	(55,848)
Ending balance, treasury stock (in shares) at Feb. 28, 2022				3,601,395
Balance, beginning of period (in shares) at Nov. 30, 2021		41,372,890
Beginning balance at Nov. 30, 2021	1,098,895	$ 414	1,094,467	$ (927,505)	989,189	(57,670)
Beginning balance, treasury stock (in shares) at Nov. 30, 2021				3,600,720
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	109,938				109,938
Other comprehensive income (loss)	1,822					1,822
Common stock issued for employee stock plans (in shares)		111,360		260
Common stock issued for employee stock plans	21,036	$ 1	21,163	$ (128)
Vesting of restricted stock (in shares)		1,011		415
Vesting of restricted stock	$ (181)			$ (181)
Repurchase of common stock (in shares)	0
Repurchases of common stock	$ 0
Stock-based compensation expense	15,536		15,536
Dividends declared	(31,065)				(31,065)
Balance, end of period (in shares) at Feb. 28, 2022		41,485,261
Ending balance at Feb. 28, 2022	$ 1,215,981	$ 415	1,131,166	$ (927,814)	1,068,062	(55,848)
Ending balance, treasury stock (in shares) at Feb. 28, 2022				3,601,395
Balance, beginning of period (in shares) at Aug. 31, 2022	38,044,756	41,653,218
Beginning balance at Aug. 31, 2022	$ 1,331,408	$ 417	1,190,350	$ (930,715)	1,179,739	(108,383)
Beginning balance, treasury stock (in shares) at Aug. 31, 2022	3,608,462			3,608,462
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	$ 268,391				268,391
Other comprehensive income (loss)	16,140					16,140
Common stock issued for employee stock plans (in shares)		226,966		410
Common stock issued for employee stock plans	43,438	$ 2	43,602	$ (166)
Vesting of restricted stock (in shares)		69,699		27,303
Vesting of restricted stock	$ (11,614)	$ 1		$ (11,615)
Repurchase of common stock (in shares)	0
Repurchases of common stock	$ 0
Stock-based compensation expense	27,500		27,500
Dividends declared	$ (68,109)				(68,109)
Balance, end of period (in shares) at Feb. 28, 2023	38,313,708	41,949,883
Ending balance at Feb. 28, 2023	$ 1,607,154	$ 420	1,261,452	$ (942,496)	1,380,021	(92,243)
Ending balance, treasury stock (in shares) at Feb. 28, 2023	3,636,175			3,636,175
Balance, beginning of period (in shares) at Nov. 30, 2022		41,848,430
Beginning balance at Nov. 30, 2022	$ 1,474,128	$ 418	1,225,947	$ (941,705)	1,282,527	(93,059)
Beginning balance, treasury stock (in shares) at Nov. 30, 2022				3,634,322
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	131,593				131,593
Other comprehensive income (loss)	816					816
Common stock issued for employee stock plans (in shares)		95,543
Common stock issued for employee stock plans	20,181	$ 1	20,180
Vesting of restricted stock (in shares)		5,910		1,853
Vesting of restricted stock	$ (790)	$ 1		$ (791)
Repurchase of common stock (in shares)	0
Repurchases of common stock	$ 0
Stock-based compensation expense	15,325		15,325
Dividends declared	$ (34,099)				(34,099)
Balance, end of period (in shares) at Feb. 28, 2023	38,313,708	41,949,883
Ending balance at Feb. 28, 2023	$ 1,607,154	$ 420	$ 1,261,452	$ (942,496)	$ 1,380,021	$ (92,243)
Ending balance, treasury stock (in shares) at Feb. 28, 2023	3,636,175			3,636,175