Goodwill and Intangibles - Schedule of Acquired Intangibles in Accompanying Consolidated Balance Sheets (Details) $ in Thousands	12 Months Ended
	Oct. 02, 2020 USD ($)
Finite-lived Intangible Assets [Roll Forward]
Beginning balance	$ 665,076
Acquired	80,010
Transfer to lease right-of-use asset as a result of adoption of ASC 842	(668)
Amortization	(90,563)
Foreign currency translation	4,485
Ending balance	$ 658,340
Weighted Average Amortization Period (years)	8 years
Customer Relationships, Contracts and Backlog
Finite-lived Intangible Assets [Roll Forward]
Beginning balance	$ 622,392
Acquired	73,558
Transfer to lease right-of-use asset as a result of adoption of ASC 842	0
Amortization	(86,401)
Foreign currency translation	4,496
Ending balance	$ 614,045
Weighted Average Amortization Period (years)	8 years
Developed Technology
Finite-lived Intangible Assets [Roll Forward]
Beginning balance	$ 40,833
Acquired	6,452
Transfer to lease right-of-use asset as a result of adoption of ASC 842	0
Amortization	(3,734)
Foreign currency translation	21
Ending balance	$ 43,572
Weighted Average Amortization Period (years)	11 years
Trade Names
Finite-lived Intangible Assets [Roll Forward]
Beginning balance	$ 1,183
Acquired	0
Transfer to lease right-of-use asset as a result of adoption of ASC 842	0
Amortization	(428)
Foreign currency translation	(32)
Ending balance	$ 723
Weighted Average Amortization Period (years)	10 years
Other Intangible Assets
Finite-lived Intangible Assets [Roll Forward]
Beginning balance	$ 668
Acquired	0
Transfer to lease right-of-use asset as a result of adoption of ASC 842	(668)
Amortization	0
Foreign currency translation	0
Ending balance	$ 0