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Goodwill and Intangibles - Schedule of Acquired Intangibles in Accompanying Consolidated Balance Sheets (Details)
$ in Thousands
6 Months Ended
Apr. 01, 2022
USD ($)
Finite-lived Intangible Assets [Roll Forward]  
Beginning balance $ 1,565,758
Amortization (95,338)
Acquired 112,361
Foreign currency translation (29,498)
Ending balance 1,553,283
Customer Relationships, Contracts and Backlog  
Finite-lived Intangible Assets [Roll Forward]  
Beginning balance 1,309,061
Amortization (86,394)
Acquired 69,574
Foreign currency translation (22,484)
Ending balance 1,269,757
Developed Technology  
Finite-lived Intangible Assets [Roll Forward]  
Beginning balance 40,020
Amortization (3,312)
Acquired 42,787
Foreign currency translation (190)
Ending balance 79,305
Trade Names  
Finite-lived Intangible Assets [Roll Forward]  
Beginning balance 216,677
Amortization (5,632)
Acquired 0
Foreign currency translation (6,824)
Ending balance $ 204,221