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Goodwill and Other Intangible Assets - Finite-Lived Intangible Assets (Details) - USD ($)
$ in Thousands
Apr. 02, 2021
Oct. 02, 2020
Finite-Lived Intangible Assets [Line Items]    
Gross Amount $ 3,027,240 $ 3,248,444
Accumulated Amortization (1,118,759) (1,315,807)
Net Amount 1,908,481 1,932,637
Customer relationship assets    
Finite-Lived Intangible Assets [Line Items]    
Gross Amount 1,970,874 2,195,700
Accumulated Amortization (1,115,565) (1,308,002)
Net Amount 855,309 887,698
Trade names    
Finite-Lived Intangible Assets [Line Items]    
Gross Amount 1,056,366 1,052,744
Accumulated Amortization (3,194) (7,805)
Net Amount $ 1,053,172 $ 1,044,939