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Basis of Presentation and Summary of Significant Accounting Policies - Narrative (Details) $ in Thousands	3 Months Ended		6 Months Ended
	Apr. 01, 2022 USD ($) country	Apr. 02, 2021 USD ($)	Apr. 01, 2022 USD ($) country segment	Apr. 02, 2021 USD ($)	Oct. 01, 2021 USD ($)
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]
Number of reportable segments | segment			3
Cash and cash equivalents	$ 429,306		$ 429,306		$ 532,591
Equity method investment, aggregate cost	273,300		273,300		224,600
Equity securities without readily determinable fair value, amount	180,500		180,500		180,500
Deferred income taxes and other liabilities	1,022,402		1,022,402		1,079,014
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		64,200
FSS United States and Uniform | Cost of services provided
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]
CARES Act. COVID-19 labor related credit		$ 39,500		$ 74,000
Uniform | Cost of services provided
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]
CARES Act. COVID-19 labor related credit		$ 4,500		$ 9,200
FSS International | Cost of services provided
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]
CARES Act. COVID-19 labor related credit	21,000		33,200
Captive
Basis of Presentation and Summary of Significant Accounting Policies [Line Items]
Cash and cash equivalents	$ 137,800		$ 137,800		$ 194,300
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

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