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, 2020	38,030,000	40,767,708
Beginning balance at Aug. 31, 2020	$ 896,375	$ 408	$ 939,067	$ (636,956)	$ 633,149	$ (39,293)
Beginning balance, treasury stock (in shares) at Aug. 31, 2020				2,737,456
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	298,528				298,528
Other comprehensive income (loss)	$ 20,035					20,035
Common stock issued for employee stock plans (in shares)	280,000	260,921		318
Common stock issued for employee stock plans	$ 46,857	$ 2	46,959	$ (104)
Vesting of restricted stock (in shares)	7,000	18,995		7,151
Vesting of restricted stock	$ (2,262)			$ (2,262)
Repurchase of common stock (in shares)	531,859			531,859
Repurchases of common stock	$ (172,210)			$ (172,210)
Stock-based compensation expense	33,355		33,355
Dividends declared	$ (89,379)				(89,379)
Balance, end of period (in shares) at May. 31, 2021	37,771,000	41,047,624
Ending balance at May. 31, 2021	$ 1,031,299	$ 410	1,019,381	$ (811,532)	842,298	(19,258)
Ending balance, treasury stock (in shares) at May. 31, 2021				3,276,784
Balance, beginning of period (in shares) at Feb. 28, 2021		40,943,660
Beginning balance at Feb. 28, 2021	980,468	$ 409	989,918	$ (753,954)	772,591	(28,496)
Beginning balance, treasury stock (in shares) at Feb. 28, 2021				3,098,662
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	100,679				100,679
Other comprehensive income (loss)	9,238					9,238
Common stock issued for employee stock plans (in shares)		103,912
Common stock issued for employee stock plans	18,435	$ 1	18,434
Vesting of restricted stock (in shares)		52		22
Vesting of restricted stock	$ (7)			$ (7)
Repurchase of common stock (in shares)	178,100			178,100
Repurchases of common stock	$ (57,571)			$ (57,571)
Stock-based compensation expense	11,029		11,029
Dividends declared	$ (30,972)				(30,972)
Balance, end of period (in shares) at May. 31, 2021	37,771,000	41,047,624
Ending balance at May. 31, 2021	$ 1,031,299	$ 410	1,019,381	$ (811,532)	842,298	(19,258)
Ending balance, treasury stock (in shares) at May. 31, 2021				3,276,784
Balance, beginning of period (in shares) at Aug. 31, 2021	37,615,419	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			3,547,773
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	$ 292,495				292,495
Other comprehensive income (loss)	$ (38,172)					(38,172)
Common stock issued for employee stock plans (in shares)	409,000	391,195		260
Common stock issued for employee stock plans	$ 74,048	$ 4	74,172	$ (128)
Vesting of restricted stock (in shares)	7,000	18,384		7,172
Vesting of restricted stock	$ (3,134)			$ (3,134)
Repurchase of common stock (in shares)	46,200			46,200
Repurchases of common stock	$ (18,639)			$ (18,639)
Stock-based compensation expense	40,604		40,604
Dividends declared	$ (95,833)				(95,833)
Balance, end of period (in shares) at May. 31, 2022	37,971,366	41,572,771
Ending balance at May. 31, 2022	$ 1,267,722	$ 416	1,163,081	$ (927,818)	1,109,177	(77,134)
Ending balance, treasury stock (in shares) at May. 31, 2022	3,601,405			3,601,405
Balance, beginning of period (in shares) at Feb. 28, 2022		41,485,261
Beginning balance at Feb. 28, 2022	$ 1,215,981	$ 415	1,131,166	$ (927,814)	1,068,062	(55,848)
Beginning balance, treasury stock (in shares) at Feb. 28, 2022				3,601,395
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	74,910				74,910
Other comprehensive income (loss)	(21,286)					(21,286)
Common stock issued for employee stock plans (in shares)		87,486
Common stock issued for employee stock plans	17,249	$ 1	17,248
Vesting of restricted stock (in shares)		24		10
Vesting of restricted stock	$ (4)			$ (4)
Repurchase of common stock (in shares)	0
Repurchases of common stock	$ 0
Stock-based compensation expense	14,667		14,667
Dividends declared	$ (33,795)				(33,795)
Balance, end of period (in shares) at May. 31, 2022	37,971,366	41,572,771
Ending balance at May. 31, 2022	$ 1,267,722	$ 416	$ 1,163,081	$ (927,818)	$ 1,109,177	$ (77,134)
Ending balance, treasury stock (in shares) at May. 31, 2022	3,601,405			3,601,405