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Goodwill and Other Intangible Assets - Finite-Lived Intangible Assets (Details) - USD ($)
$ in Thousands
Jul. 02, 2021
Oct. 02, 2020
Finite-Lived Intangible Assets [Line Items]    
Gross Amount $ 3,211,947 $ 3,248,444
Accumulated Amortization (1,147,671) (1,315,807)
Net Amount 2,064,276 1,932,637
Customer relationship assets    
Finite-Lived Intangible Assets [Line Items]    
Gross Amount 2,105,334 2,195,700
Accumulated Amortization (1,143,813) (1,308,002)
Net Amount 961,521 887,698
Trade names    
Finite-Lived Intangible Assets [Line Items]    
Gross Amount 1,106,613 1,052,744
Accumulated Amortization (3,858) (7,805)
Net Amount $ 1,102,755 $ 1,044,939