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Basis of Presentation and Summary of Significant Accounting Policies - Narrative (Details)
$ in Thousands
 3 Months Ended 12 Months Ended
Dec. 29, 2023
USD ($)
segment
country
Dec. 30, 2022
USD ($)
Sep. 29, 2023
USD ($)
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]      
Number of reportable segments | segment 2    
Foreign currency transaction loss $ 3,900 $ 1,100  
Cash and cash equivalents 295,597 288,228 $ 1,927,088
Impairment charges 0 18,316  
Equity method investment, aggregate cost 71,200   73,500
Equity securities without readily determinable fair value, amount 83,600   83,600
Supplier finance program, obligation 3,100   2,800
Pension plan adjustments from spin-off 5,100    
Foreign currency translation adjustments, spin-off 26,300    
Cost of services provided | FSS United States and Uniform      
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]      
Impairment charges   18,300  
Cost of services provided | FSS - United States | Right Of Use Assets      
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]      
Impairment charges   7,900  
Cost of services provided | FSS - United States | Leasehold Improvements      
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]      
Impairment charges   $ 10,400  
Deferred Income Taxes and Other Noncurrent Liabilities | CARES Act      
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]      
Payment of deferred social security taxes     47,600
Captive      
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]      
Cash and cash equivalents 14,400   32,800
Captive | Prepaid Expenses and Other Current Assets      
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]      
Investment at cost $ 111,700   $ 110,700
Foreign Countries Outside North America      
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]      
Number of foreign countries in which entity operates | country 14