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Business Segments - Reconciliation of Segments Assets to Consolidated (Details) - USD ($)
$ in Thousands
 12 Months Ended
Oct. 03, 2025
Sep. 27, 2024
Sep. 29, 2023
Segment Reporting Information [Line Items]      
Capital Expenditures and Other $ 499,300 $ 454,600 $ 385,000
Depreciation and amortization 476,345 435,547 409,857
Identifiable Assets 13,304,629 12,674,371  
FSS United States      
Segment Reporting Information [Line Items]      
Depreciation and amortization 282,600 269,500 265,600
FSS International      
Segment Reporting Information [Line Items]      
Depreciation and amortization 68,400 58,900 54,600
Operating Segments | FSS United States      
Segment Reporting Information [Line Items]      
Capital Expenditures and Other 389,500 359,400 299,300
Depreciation and amortization 380,600 360,900 342,400
Identifiable Assets 10,181,800 9,903,200  
Operating Segments | FSS International      
Segment Reporting Information [Line Items]      
Capital Expenditures and Other 109,800 95,200 85,300
Depreciation and amortization 94,900 74,600 67,300
Identifiable Assets 3,030,500 2,586,400  
Corporate      
Segment Reporting Information [Line Items]      
Capital Expenditures and Other 0 0 400
Depreciation and amortization 800 0 $ 200
Identifiable Assets $ 92,300 $ 184,800