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Equity - Additional Information (Detail) - USD ($)
12 Months Ended
Aug. 31, 2025
Aug. 31, 2024
Aug. 31, 2023
Jan. 08, 2025
Stockholders Equity Note [Line Items]        
Shares available for grant 800,000 1,000,000 1,200,000  
Performance based share based compensation and dividend equivalent rights 312,000 [1] 400,000 500,000  
Percentage of weighted EBITDA 60.00% 60.00% 60.00%  
percentage of weighted ROIC 20.00% 20.00% 20.00%  
Percentage of weighted peer group TSR 20.00% 20.00% 20.00%  
Authorized amount under stock repurchase program $ 100,000,000      
Unamortized compensation cost of restricted stock unit grants $ 18,000,000      
Unamortized compensation cost of restricted stock unit grants expected to be recognized over weighted average period 2 years      
Number of shares repurchased   38,000 1,900,000  
Share repurchase program, current authorization of shares purchased 517,000      
Number of shares repurchased amount   $ 1,300,000 $ 56,900,000  
Share repurchase program, current authorization of shares purchased amount $ 22,200,000      
Accrued excise taxes 100,000 0 500,000  
Remaining authorized repurchase amount $ 77,800,000     $ 100,000,000
Repurchase program expiration date Jan. 31, 2027      
Selling, Administrative and Cost of Revenue        
Stockholders Equity Note [Line Items]        
Restricted stock compensation expense $ 17,500,000 17,100,000 12,100,000  
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 400,000      
Unvested Restricted Stock Grants        
Stockholders Equity Note [Line Items]        
Fair value of awards granted $ 17,500,000 $ 17,300,000 $ 12,400,000  
2021 Stock Incentive Plan        
Stockholders Equity Note [Line Items]        
Number of shares authorized 2,200,000      
2017 Amended and Restated Stock Incentive Plan        
Stockholders Equity Note [Line Items]        
Number of shares reserved 700,000      
[1] Includes 143 thousand time-based and 169 thousand performance-based restricted stock unit awards.