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Basis of Presentation and Summary of Significant Accounting Policies - Narrative (Details)
$ in Thousands
 3 Months Ended 9 Months Ended
May 16, 2023
USD ($)
Apr. 06, 2023
USD ($)
Jun. 30, 2023
USD ($)
country
Jul. 01, 2022
USD ($)
Jun. 30, 2023
USD ($)
segment
country
Jul. 01, 2022
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Sep. 30, 2022
USD ($)
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]              
Number of reportable segments | segment         3    
Foreign currency transaction loss     $ 2,800 $ 1,200 $ 6,700 $ 2,200  
Cash and cash equivalents     402,414   402,414   $ 329,452
Impairment charges         35,479 0  
Equity method investment, aggregate cost     98,000   98,000   224,500
Gain (loss) on equity method investment     377,100   (275,900)    
Proceeds from sale of equity investments $ 98,200       633,179 0  
Pre-tax loss on sale of equity investment     1,100   1,100    
Loss on sale of equity investment, net of tax     2,200   2,200    
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%          
Proceeds from sale of equity method investments   $ 535,000          
Equity securities without readily determinable fair value, amount     85,200   85,200   180,500
Cost of services provided | FSS United States and Uniform              
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]              
Impairment charges         26,700    
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    
Cost of services provided | Uniform | Right Of Use Assets              
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]              
Impairment charges         7,100    
Cost of services provided | Uniform | Other Assets              
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]              
Impairment charges         600    
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 $ 64,200  
Captive              
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]              
Cash and cash equivalents     24,400   24,400   23,100
Captive | Prepaid Expenses and Other Current Assets              
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]              
Investment at cost     $ 109,800   $ 109,800   $ 78,200
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     18   18