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Basis of Presentation and Summary of Significant Accounting Policies - Narrative (Details)
 3 Months Ended 6 Months Ended 12 Months Ended
Mar. 29, 2024
USD ($)
country
Mar. 31, 2023
USD ($)
Mar. 29, 2024
USD ($)
segment
country
Mar. 31, 2023
USD ($)
Sep. 29, 2023
USD ($)
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]          
Number of reportable segments | segment     2    
Pension plan adjustments from spin-off     $ 5,100,000    
Foreign currency translation adjustments, spin-off     26,300,000    
Foreign currency transaction loss $ 900,000 $ 2,800,000 4,800,000 $ 3,900,000  
Cash and cash equivalents 356,605,000 292,199,000 356,605,000 292,199,000 $ 1,927,088,000
Impairment charges     0 27,781,000  
Equity method investment, aggregate cost 71,600,000   71,600,000   73,500,000
Equity securities without readily determinable fair value, amount 83,600,000   83,600,000   83,600,000
Supplier finance program, obligation 2,200,000   2,200,000   2,800,000
Cost of services provided | FSS - United States          
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]          
Impairment charges   700,000   19,000,000  
Cost of services provided | FSS - United States | Right Of Use Assets          
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]          
Impairment charges   700,000   8,600,000  
Cost of services provided | FSS - United States | Leasehold Improvements          
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]          
Impairment charges   $ 0   $ 10,400,000  
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         47,600,000
Captive          
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]          
Cash and cash equivalents 13,200,000   13,200,000   32,800,000
Captive | Prepaid Expenses and Other Current Assets          
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]          
Investment at cost $ 112,800,000   $ 112,800,000   $ 110,700,000
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   14