Goodwill and Other Intangible Assets - Schedule of Intangible Assets, Net (Details) - USD ($) $ in Thousands	Mar. 01, 2025	Aug. 31, 2024
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	$ 436,170	$ 435,754
Accumulated Amortization	325,230	315,755
Net Carrying Amount	110,940	119,999
Customer Contracts
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	315,833	314,446
Accumulated Amortization	235,714	228,456
Net Carrying Amount	80,119	85,990
Software
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	80,626	81,482
Accumulated Amortization	52,434	51,023
Net Carrying Amount	28,192	30,459
Other Intangible Assets
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	39,711	39,826
Accumulated Amortization	37,082	36,276
Net Carrying Amount	$ 2,629	$ 3,550