Goodwill and Other Intangible Assets - Schedule of Intangible Assets, Net (Details) - USD ($) $ in Thousands	Aug. 31, 2024	Aug. 26, 2023
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	$ 435,754	$ 439,584
Accumulated Amortization	315,755	293,966
Net Carrying Amount	119,999	145,618
Customer Contracts
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	314,446	315,448
Accumulated Amortization	228,456	211,996
Net Carrying Amount	85,990	103,452
Software
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	81,482	80,538
Accumulated Amortization	51,023	45,117
Net Carrying Amount	30,459	35,421
Other Intangible Assets
Finite-Lived Intangible Assets [Line Items]
Gross Carrying Amount	39,826	43,598
Accumulated Amortization	36,276	36,853
Net Carrying Amount	$ 3,550	$ 6,745