Leases (Supplemental Cash Flow) (Details) - USD ($) $ in Thousands	12 Months Ended
	Aug. 31, 2026	Aug. 31, 2025	Aug. 31, 2024
Leases [Abstract]
Operating Lease, Payments	$ 13,000	$ 12,500	$ 12,100
Right-of-Use Asset Obtained in Exchange for Operating Lease Liability	$ 4,900	$ 6,200	$ 3,100
Operating Lease, Right-of-Use Asset, Statement of Financial Position [Extensible Enumeration]	Other Assets, Noncurrent	Other Assets, Noncurrent