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Nature of Business, Basis of Presentation and Summary of Significant Accounting Policies - Narrative (Details)
$ in Thousands
 2 Months Ended 12 Months Ended
Sep. 22, 2023
USD ($)
May 16, 2023
USD ($)
Apr. 06, 2023
USD ($)
Nov. 21, 2023
USD ($)
Sep. 29, 2023
USD ($)
segment
country
Sep. 30, 2022
USD ($)
Oct. 01, 2021
USD ($)
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]              
Number of countries in which entity operates | country         14    
Number of reportable segments | segment         3    
Foreign currency transaction loss         $ 10,400 $ 3,500 $ 1,800
Cash and cash equivalents         1,963,139 329,452  
Inventory valuation reserves         21,000 51,300  
Inventory write-down           19,600 25,400
Depreciation         371,700 367,100 378,300
Asset write-downs         37,563 0 0
Equity Securities, FV-NI         99,300 224,500  
Pre-tax gain on sale of equity investment $ 51,800 $ (1,100)     377,100    
Gain on sale of this equity investment         278,700    
Equity Securities without readily determinable fair value, amount         85,100 180,500  
Proceeds from sale of equity investments $ 51,900 98,200     685,048 0 0
Loss on sale of equity investment, net of tax   $ 2,200          
Gain on Equity Investments, net         (427,803) 0 (137,934)
Deferred income taxes and other liabilities         1,161,805 1,106,587  
Total future minimum lease payments         193,321    
Payments related to tax withholding for share-based compensation         $ 31,300 17,800 24,500
AIM Services Co., Ltd | AIM Services Co., Ltd              
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]              
Ownership percentage     50.00%   50.00%    
Proceeds from sale of equity method investments     $ 535,000        
Captive              
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]              
Cash and cash equivalents         $ 32,800 23,100  
Cost of services provided (exclusive of depreciation and amortization)              
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]              
CARES Act. COVID-19 labor related credits             15,100
Property and Equipment and Long-term Borrowings              
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]              
Total future minimum lease payments         47,500 35,800 $ 36,000
Prepaid expenses and other current assets | Captive              
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]              
Investment at cost         110,700 78,200  
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           64,200  
Deferred income taxes and other liabilities         64,200    
Accounts Receivable | CARES Act Receivables | Government              
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]              
CARES act. receivables         20,400    
FSS United States and Uniform | Cost of services provided (exclusive of depreciation and amortization)              
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]              
Asset write-downs         26,700    
CARES Act. COVID-19 labor related credits         37,000 155,300  
Uniform              
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]              
Restructuring charges         51,100 9,300  
Uniform | Cost of services provided (exclusive of depreciation and amortization)              
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]              
CARES Act. COVID-19 labor related credits         400 $ 17,900  
Uniform | Subsequent Event              
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]              
Restructuring charges       $ 20,000      
Right of Use Assets | FSS United States | Cost of services provided (exclusive of depreciation and amortization)              
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]              
Asset write-downs         8,600    
Right of Use Assets | Uniform | Cost of services provided (exclusive of depreciation and amortization)              
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]              
Asset write-downs         7,100    
Leasehold Improvements | FSS United States | Cost of services provided (exclusive of depreciation and amortization)              
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]              
Asset write-downs         $ 10,400    
Building and Building Improvements | Minimum              
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]              
Property, plant and equipment, estimated useful lives         10 years    
Building and Building Improvements | Maximum              
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]              
Property, plant and equipment, estimated useful lives         40 years    
Service Equipment and Fixtures | Minimum              
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]              
Property, plant and equipment, estimated useful lives         3 years    
Service Equipment and Fixtures | Maximum              
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]              
Property, plant and equipment, estimated useful lives         20 years    
Other Assets | Uniform | Cost of services provided (exclusive of depreciation and amortization)              
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]              
Asset write-downs         $ 600