Goodwill and Intangible Assets - Gross Amount and Accumulated Amortization of Acquired Finite-lived Intangibles (Details) - USD ($) $ in Thousands	12 Months Ended
	Oct. 03, 2021	Sep. 27, 2020
Finite-Lived Intangible Assets [Line Items]
Gross Amount	$ 118,971	$ 106,421
Accumulated Amortization	(80,981)	(92,478)
Net Amount	$ 37,990	13,943
Client relations
Finite-Lived Intangible Assets [Line Items]
Weighted- Average Remaining Life (in years)	7 years 3 months 18 days
Gross Amount	$ 69,455	60,775
Accumulated Amortization	(43,984)	(53,392)
Net Amount	$ 25,471	7,383
Backlog
Finite-Lived Intangible Assets [Line Items]
Weighted- Average Remaining Life (in years)	8 months 12 days
Gross Amount	$ 34,577	37,682
Accumulated Amortization	(30,670)	(32,761)
Net Amount	$ 3,907	4,921
Technology and trade names
Finite-Lived Intangible Assets [Line Items]
Weighted- Average Remaining Life (in years)	3 years 9 months 18 days
Gross Amount	$ 14,939	7,964
Accumulated Amortization	(6,327)	(6,325)
Net Amount	$ 8,612	$ 1,639