Business Combinations, Asset Acquisitions, and Joint Venture Formation (Details) $ in Thousands, € in Millions		3 Months Ended		9 Months Ended
	Sep. 04, 2024 USD ($)	May 31, 2025 USD ($)	May 31, 2024 USD ($)	May 31, 2025 USD ($)	May 31, 2024 USD ($)	May 31, 2025 EUR (€)	Sep. 04, 2024 EUR (€)	Aug. 31, 2024 USD ($)
Business Combination, Asset Acquisition, Transaction between Entities under Common Control, and Joint Venture Formation [Abstract]
Goodwill, Acquired During Period				$ 14,846
Net Sales		$ 158,661	$ 150,389	449,385	$ 430,796
Business Combination [Line Items]
Net Sales		158,661	$ 150,389	449,385	430,796
Goodwill, Acquired During Period				14,846
Payments to Acquire Businesses, Net of Cash Acquired				26,744	$ 0
Goodwill		$ 287,630		$ 287,630				$ 269,597
Developed Technology
Business Combination [Line Items]
Weighted Average Amortization Period (Years)		10 years		10 years		10 years
Customer Relationships
Business Combination [Line Items]
Weighted Average Amortization Period (Years)		14 years		14 years		14 years
Technology-Based Intangible Assets
Business Combination [Line Items]
Weighted Average Amortization Period (Years)		14 years		14 years		14 years
DTA
Business Combination, Asset Acquisition, Transaction between Entities under Common Control, and Joint Venture Formation [Abstract]
Business Combination, Contingent Consideration, Range of Outcomes, Maximum, Amount | €							€ 36.0
Business Combination, Recognized Asset Acquired, Property, Plant, and Equipment		$ 2,841		$ 2,841
Business Combination [Line Items]
Business Combination, Contingent Consideration, Range of Outcomes, Maximum, Amount | €							36.0
Business Combination, Recognized Asset Acquired, Property, Plant, and Equipment		2,841		2,841
Payments to Acquire Businesses, Net of Cash Acquired	$ 26,700
Business Combination, Contingent Consideration, Liability | €						€ 2.3	€ 12.0
Business Combination, Recognized Asset Acquired, Identifiable Intangible Asset, Excluding Goodwill		14,977		14,977
Goodwill		14,846		14,846
DTA | Developed Technology
Business Combination [Line Items]
Business Combination, Recognized Asset Acquired, Identifiable Intangible Asset, Finite-Lived		$ 1,600		$ 1,600
Weighted Average Amortization Period (Years)		3 years		3 years		3 years
DTA | Customer Relationships
Business Combination [Line Items]
Business Combination, Recognized Asset Acquired, Identifiable Intangible Asset, Finite-Lived		$ 3,600		$ 3,600
Weighted Average Amortization Period (Years)		14 years		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		$ 9,800
Weighted Average Amortization Period (Years)		14 years		14 years		14 years