Business Combinations, Asset Acquisitions, and Joint Venture Formation (Details) $ in Thousands, € in Millions	3 Months Ended
	Nov. 30, 2024 USD ($)	Nov. 30, 2024 EUR (€)	Nov. 30, 2023 USD ($)	Sep. 04, 2024 EUR (€)
Business Combination, Asset Acquisition, and Joint Venture Formation [Abstract]
Goodwill, Acquired During Period | $	$ 23,105
Net Sales | $	145,196		$ 141,970
Business Acquisition [Line Items]
Net Sales | $	145,196		141,970
Goodwill, Acquired During Period | $	23,105
Payments to Acquire Businesses, Net of Cash Acquired | $	27,196		$ 0
DTA
Business Combination, Asset Acquisition, and Joint Venture Formation [Abstract]
Business Combination, Contingent Consideration Arrangements, Range of Outcomes, Value, High				€ 36.0
Goodwill, Acquired During Period		€ 22.0
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Property, Plant, and Equipment		3.0
Net Sales		3.2
Business Acquisition [Line Items]
Net Sales		3.2
Business Combination, Contingent Consideration Arrangements, Range of Outcomes, Value, High				€ 36.0
Goodwill, Acquired During Period		22.0
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Property, Plant, and Equipment		€ 3.0
Payments to Acquire Businesses, Net of Cash Acquired | $	$ 27,200