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, 2022		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
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		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
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		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
Balance, beginning of period (in shares) at Aug. 31, 2023	38,025,372	42,096,628
Beginning balance at Aug. 31, 2023	$ 1,619,930	$ 421	1,323,631	$ (1,122,077)	1,505,096	(87,141)
Beginning balance, treasury stock (in shares) at Aug. 31, 2023	4,071,256			4,071,256
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	$ 289,495				289,495
Other comprehensive income (loss)	(3,888)					(3,888)
Common stock issued for employee stock plans (in shares)		297,348		343
Common stock issued for employee stock plans	66,391	$ 3	66,541	$ (153)
Vesting of restricted stock (in shares)		81,750		32,040
Vesting of restricted stock	$ (14,312)	$ 1	(1)	$ (14,312)
Repurchase of common stock (in shares)	249,000			249,000
Repurchases of common stock	$ (112,165)			$ (112,165)
Stock-based compensation expense	30,962		30,962
Dividends declared	$ (74,659)				(74,659)
Balance, end of period (in shares) at Feb. 29, 2024	38,123,087	42,475,726
Ending balance at Feb. 29, 2024	$ 1,801,754	$ 425	1,421,133	$ (1,248,707)	1,719,932	(91,029)
Ending balance, treasury stock (in shares) at Feb. 29, 2024	4,352,639			4,352,639
Balance, beginning of period (in shares) at Nov. 30, 2023		42,297,330
Beginning balance at Nov. 30, 2023	$ 1,700,740	$ 423	1,366,343	$ (1,195,491)	1,616,352	(86,887)
Beginning balance, treasury stock (in shares) at Nov. 30, 2023				4,237,590
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	140,940				140,940
Other comprehensive income (loss)	(4,142)					(4,142)
Common stock issued for employee stock plans (in shares)		172,244		197
Common stock issued for employee stock plans	38,052	$ 2	38,138	$ (88)
Vesting of restricted stock (in shares)		6,152		1,802
Vesting of restricted stock	$ (873)			$ (873)
Repurchase of common stock (in shares)	113,050			113,050
Repurchases of common stock	$ (52,255)			$ (52,255)
Stock-based compensation expense	16,652		16,652
Dividends declared	$ (37,360)				(37,360)
Balance, end of period (in shares) at Feb. 29, 2024	38,123,087	42,475,726
Ending balance at Feb. 29, 2024	$ 1,801,754	$ 425	$ 1,421,133	$ (1,248,707)	$ 1,719,932	$ (91,029)
Ending balance, treasury stock (in shares) at Feb. 29, 2024	4,352,639			4,352,639