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Basis of Presentation and Summary of Significant Accounting Policies - Narrative (Details)
$ in Thousands
 3 Months Ended 9 Months Ended
Jun. 28, 2024
USD ($)
country
Jun. 30, 2023
USD ($)
Jun. 28, 2024
USD ($)
segment
country
Jun. 30, 2023
USD ($)
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    
Foreign currency translation adjustments, spin-off     26,300    
Cash and cash equivalents $ 436,075 $ 388,166 436,075 $ 388,166 $ 1,927,088
Impairment charges     0 27,781  
Equity method investment, aggregate cost 75,400   75,400   73,500
Pre-tax gain (loss) on sale of equity investment   1,100   1,100  
Equity securities without readily determinable fair value, amount 83,600   83,600   83,600
Proceeds from sale of equity investments   98,200 0 633,179  
Loss on sale of equity investment, net of tax   2,200   2,200  
Supplier finance program, obligation 2,900   2,900   2,800
Payment of deferred social security taxes       47,600  
Equity Method Investments          
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]          
Pre-tax gain (loss) on sale of equity investment   (377,100)   (377,100)  
Gain on sale of this equity investment   $ 275,900   $ 275,900  
AIM Services Co., Ltd | AIM Services Co., Ltd          
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]          
Equity method investment, ownership interest, percent   50.00%   50.00%  
Proceeds from sale of equity method investments   $ 535,000      
Cost of services provided | FSS United States          
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]          
Impairment charges       $ 19,000  
Cost of services provided | FSS United States | Right Of Use Assets          
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]          
Impairment charges       8,600  
Cost of services provided | FSS United States | Leasehold Improvements          
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]          
Impairment charges       10,400  
Captive          
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]          
Cash and cash equivalents 15,700   15,700   32,800
Investment at cost $ 114,300   $ 114,300   $ 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   14    
ARGENTINA          
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]          
Foreign currency transaction loss $ 400 $ 2,800 $ 5,200 $ 6,700