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Business Segments - Narrative (Details)
$ in Thousands
12 Months Ended
Sep. 29, 2023
USD ($)
segment
Sep. 30, 2022
USD ($)
Oct. 01, 2021
USD ($)
Apr. 06, 2023
Segment Reporting Information [Line Items]        
Number of reportable segments | segment 3      
Gain on Equity Investments, net (see Note 1) $ (427,803) $ 0 $ (137,934)  
Equity securities without readily determined fair value, recognized non-cash gain on price change     (137,900)  
Loss on defined benefit pension plan termination $ 0 0 60,864  
AIM Services Co., Ltd | AIM Services Co., Ltd        
Segment Reporting Information [Line Items]        
Ownership percentage 50.00%     50.00%
Gain on Equity Investments, net (see Note 1) $ (427,800)      
Cost of services provided (exclusive of depreciation and amortization) | FSS United States        
Segment Reporting Information [Line Items]        
Gain on investments $ 36,300 $ 19,000 $ 10,000  
Food Services | Sales Revenue, Segment | Product Concentration Risk        
Segment Reporting Information [Line Items]        
Concentration risk, percentage 74.00%      
Facilities & Other | Sales Revenue, Segment | Product Concentration Risk        
Segment Reporting Information [Line Items]        
Concentration risk, percentage 26.00%