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 ($)	Aug. 31, 2025 USD ($)	Aug. 31, 2024 USD ($)	Aug. 31, 2023 USD ($)	Aug. 31, 2025 EUR (€)	Sep. 04, 2024 EUR (€)
Business Combination [Line Items]
Goodwill, Acquired During Period		$ 14,684
Payments to Acquire Businesses, Net of Cash Acquired		26,661	$ 0	$ 0
Goodwill		$ 289,787	$ 269,597	$ 266,494
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 | €					€ 2.5	€ 2.3
Payments to Acquire Businesses, Net of Cash Acquired	$ 26,700
Business Combination, Recognized Asset Acquired, Asset, Current	6,299
Business Combination, Recognized Asset Acquired, Property, Plant, and Equipment	2,841
Goodwill	14,684
Business Combination, Recognized Asset Acquired, Asset, Noncurrent	400
Business Combination, Recognized Liability Assumed, Liability, Current	6,977
Business Combination, Recognized Liability Assumed, Liability, Noncurrent	5,563
Business Combination, Recognized Asset Acquired to Liability Assumed, Excess (Less)	26,661
Business Combination, Recognized Asset Acquired, Asset	39,201
Business Combination, Recognized Asset Acquired, Identifiable Intangible Asset, Excluding Goodwill	14,977	$ 15,000
Business Combination, Contingent Consideration, Range of Outcomes, Maximum, Amount | €						36.0
DTA | Maximum
Business Combination [Line Items]
Business Combination, Contingent Consideration, Liability | €						€ 12.0
DTA | Trademarks and Tradenames
Business Combination [Line Items]
Business Combination, Recognized Asset Acquired, Identifiable Intangible Asset, Finite-Lived	$ 1,700
Weighted Average Amortization Period	3 years					3 years
DTA | Customer Relationships
Business Combination [Line Items]
Business Combination, Recognized Asset Acquired, Identifiable Intangible Asset, Finite-Lived	$ 3,600
Weighted Average Amortization Period	14 years					14 years
DTA | Technology-Based Intangible Assets
Business Combination [Line Items]
Business Combination, Recognized Asset Acquired, Identifiable Intangible Asset, Finite-Lived	$ 9,800
Weighted Average Amortization Period	7 years					7 years