Leases (Supplemental Balance Sheet) (Details) - USD ($) $ in Thousands	Aug. 31, 2024	Aug. 31, 2023
Leases [Abstract]
Operating Lease, Right-of-Use Asset	$ 32,961	$ 37,714
Operating Lease, Liability, Current	9,464	9,786
Operating Lease, Liability, Noncurrent	$ 25,154	$ 29,245
Operating Lease, Weighted Average Remaining Lease Term	7 years	6 years 6 months
Operating Lease, Weighted Average Discount Rate, Percent	5.50%	5.00%
Operating Leased Assets [Line Items]
Operating Lease, Liability, Noncurrent	$ 25,154	$ 29,245
Operating Lease, Liability, Current	9,464	9,786
Operating Lease, Right-of-Use Asset	$ 32,961	$ 37,714
Operating Lease, Liability, Noncurrent, Statement of Financial Position [Extensible Enumeration]	Other long-term liabilities	Other long-term liabilities
Operating Lease, Liability, Statement of Financial Position [Extensible Enumeration]	Other Liabilities	Other Liabilities
Operating Lease, Weighted Average Remaining Lease Term	7 years	6 years 6 months
Operating Lease, Weighted Average Discount Rate, Percent	5.50%	5.00%
Operating Lease, Right-of-Use Asset, Statement of Financial Position [Extensible Enumeration]	Other Assets, Noncurrent	Other Assets, Noncurrent
Operating Lease, Liability, Current, Statement of Financial Position [Extensible Enumeration]	Other current liabilities	Other current liabilities
Other Noncurrent Liabilities
Operating Leased Assets [Line Items]
Operating Lease, Liability, Statement of Financial Position [Extensible Enumeration]	Other Liabilities