Fair Value Measures - Carrying Value and Estimated Carrying Value and Fair Value of Financial Instruments (Details) - USD ($) $ in Thousands	Nov. 30, 2023	Aug. 31, 2023
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Total unamortized discounts and debt issuance costs	$ (11,366)	$ (12,300)
Total net carrying value of debt	1,551,134	1,612,700
Principal Amount
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Long-term debt, fair value	1,562,500	1,625,000
Principal Amount | Level 1 | Senior Notes | 2027 Notes
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Long-term debt, fair value	500,000	500,000
Principal Amount | Level 1 | Senior Notes | 2032 Notes
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Long-term debt, fair value	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]
Long-term debt, fair value	312,500	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]
Long-term debt, fair value	250,000	250,000
Estimated Fair Value
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Long-term debt, fair value	1,446,444	1,507,871
Estimated Fair Value | Level 1 | Senior Notes | 2027 Notes
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Long-term debt, fair value	461,435	460,890
Estimated Fair Value | Level 1 | Senior Notes | 2032 Notes
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Long-term debt, fair value	425,790	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]
Long-term debt, fair value	313,281	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]
Long-term debt, fair value	$ 245,938	$ 246,875