Fair Value Measures - Carrying Value and Estimated Carrying Value and Fair Value of Financial Instruments (Details) - USD ($) $ in Thousands	Feb. 29, 2024	Aug. 31, 2023
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Total unamortized discounts and debt issuance costs	$ (10,512)	$ (12,300)
Total net carrying value of debt	1,489,488	1,612,700
Principal Amount
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Total principal amount	1,500,000	1,625,000
Principal Amount | Level 1 | Senior Notes | 2027 Notes
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Total principal amount	500,000	500,000
Principal Amount | Level 1 | Senior Notes | 2032 Notes
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Total principal amount	500,000	500,000
Principal Amount | Level 3 | Line of Credit | 2022 Credit Agreement | Term Loan
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Total principal amount	250,000	375,000
Principal Amount | Level 3 | Line of Credit | 2022 Credit Agreement | Revolving Credit Facility
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Total principal amount	250,000	250,000
Estimated Fair Value
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Total principal amount	1,399,591	1,507,871
Estimated Fair Value | Level 1 | Senior Notes | 2027 Notes
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Total principal amount	465,950	460,890
Estimated Fair Value | Level 1 | Senior Notes | 2032 Notes
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Total principal amount	434,735	423,700
Estimated Fair Value | Level 3 | Line of Credit | 2022 Credit Agreement | Term Loan
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Total principal amount	251,093	376,406
Estimated Fair Value | Level 3 | Line of Credit | 2022 Credit Agreement | Revolving Credit Facility
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Total principal amount	$ 247,813	$ 246,875