Business Combinations, Asset Acquisitions, Transaction between Entities under Common Control, and Joint Venture Formation (Details) $ in Thousands, € in Millions		12 Months Ended
	Sep. 04, 2024 USD ($)	Aug. 31, 2026 USD ($)	Aug. 31, 2025 USD ($)	Aug. 31, 2024 USD ($)	Aug. 31, 2026 EUR (€)	Aug. 31, 2025 EUR (€)	Sep. 04, 2024 EUR (€)
Business Combination [Line Items]
Payments to Acquire Businesses, Net of Cash Acquired		$ 0	$ 26,700	$ 0
Goodwill		$ 289,700	$ 289,800	$ 269,600
Trademarks and Tradenames
Business Combination [Line Items]
Weighted Average Amortization Period		7 years			7 years
Customer Relationships
Business Combination [Line Items]
Weighted Average Amortization Period		14 years			14 years
Technology-Based Intangible Assets
Business Combination [Line Items]
Weighted Average Amortization Period		7 years			7 years
DTA
Business Combination [Line Items]
Business Combination, Contingent Consideration, Liability | €					€ 2.9	€ 2.5
Payments to Acquire Businesses, Net of Cash Acquired	$ 26,700
Business Combination, Effective Date of Acquisition	Sep. 04, 2024
DTA | Maximum
Business Combination [Line Items]
Business Combination, Contingent Consideration, Liability | €							€ 12.0