Goodwill and Intangible Assets - Gross Amount and Accumulated Amortization of Acquired Finite-lived Intangibles (Details) - USD ($) $ in Thousands	6 Months Ended
	Apr. 03, 2022	Oct. 03, 2021
Finite-Lived Intangible Assets [Line Items]
Gross Amount	$ 97,165	$ 118,971
Accumulated Amortization	(57,685)	(80,981)
Net Amount	$ 39,480	37,990
Client relations
Finite-Lived Intangible Assets [Line Items]
Weighted- Average Remaining Life (in Years)	5 years 10 months 24 days
Gross Amount	$ 46,519	69,455
Accumulated Amortization	(20,069)	(43,984)
Net Amount	$ 26,450	25,471
Backlog
Finite-Lived Intangible Assets [Line Items]
Weighted- Average Remaining Life (in Years)	1 year
Gross Amount	$ 35,742	34,577
Accumulated Amortization	(30,024)	(30,670)
Net Amount	$ 5,718	3,907
Technology and trade names
Finite-Lived Intangible Assets [Line Items]
Weighted- Average Remaining Life (in Years)	4 years 1 month 6 days
Gross Amount	$ 14,904	14,939
Accumulated Amortization	(7,592)	(6,327)
Net Amount	$ 7,312	$ 8,612