Equity - Additional Information (Detail) - USD ($)		12 Months Ended
	Jan. 05, 2023	Aug. 31, 2023	Aug. 31, 2022	Aug. 31, 2021	Jan. 06, 2021
Stockholders Equity Note [Line Items]
Shares repurchased		$ 56,900,000		$ 20,000,000
Shares available for grant		1,200	1,400	1,600
Performance based share based compensation and dividend equivalent rights		450,000	400,000	500,000
Share based compensation, non vested shares		972,000	1,042,000
Percentage of weighted EBITDA		60.00%	80.00%	80.00%
percentage of weighted ROIC		20.00%	20.00%	20.00%
Percentage of weighted peer group TSR		20.00%
Number of authorized shares repurchased			0	0
Authorized amount under stock repurchase program		$ 100,000,000
Unamortized compensation cost of restricted stock unit grants		$ 11,800,000
Number of shares repurchased		1,900,000
Share repurchase program, current authorization of shares purchased		1,800,000
Number of shares repurchased amount		$ 56,900,000		$ 20,000,000
Share repurchase program, current authorization of shares purchased amount		53,600,000
Accrued excise taxes		500,000
Remaining authorized repurchase amount		46,400,000
Repurchase program expiration date	Jan. 31, 2025
Selling, Administrative and Cost of Revenue
Stockholders Equity Note [Line Items]
Restricted stock compensation expense		$ 12,100,000	$ 15,500,000	14,700,000
Minimum
Stockholders Equity Note [Line Items]
Payout percentage		0.00%
Vesting period of compensation expense		1 year
Maximum
Stockholders Equity Note [Line Items]
Payout percentage		200.00%
Vesting period of compensation expense		3 years
Restricted Stock
Stockholders Equity Note [Line Items]
Restricted stock shares issued net of shares for tax withholdings		300,000
Unvested Restricted Stock Grants
Stockholders Equity Note [Line Items]
Fair value of awards granted		$ 12,400,000	$ 18,700,000	$ 18,000,000
2021 Stock Incentive Plan and 2017 Amended and Restated Stock Incentive Plan
Stockholders Equity Note [Line Items]
Number of shares reserved for future issuance					1,500
2021 Stock Incentive Plan and 2017 Amended and Restated Stock Incentive Plan | Maximum
Stockholders Equity Note [Line Items]
Shares available for grant					500,000
Number of common shares outstanding					900,000