Goodwill and Intangible Assets - Gross Amount and Accumulated Amortization of Acquired Finite-lived Intangibles (Details) - USD ($) $ in Thousands	12 Months Ended
	Oct. 02, 2022	Oct. 03, 2021
Finite-Lived Intangible Assets [Line Items]
Gross Amount	$ 87,673	$ 118,971
Accumulated Amortization	(58,510)	(80,981)
Net Amount	$ 29,163	37,990
Client relations
Finite-Lived Intangible Assets [Line Items]
Weighted- Average Remaining Life (in years)	5 years 6 months
Gross Amount	$ 41,676	69,455
Accumulated Amortization	(21,092)	(43,984)
Net Amount	$ 20,584	25,471
Backlog
Finite-Lived Intangible Assets [Line Items]
Weighted- Average Remaining Life (in years)	7 months 6 days
Gross Amount	$ 33,286	34,577
Accumulated Amortization	(29,990)	(30,670)
Net Amount	$ 3,296	3,907
Technology and trade names
Finite-Lived Intangible Assets [Line Items]
Weighted- Average Remaining Life (in years)	3 years 8 months 12 days
Gross Amount	$ 12,711	14,939
Accumulated Amortization	(7,428)	(6,327)
Net Amount	$ 5,283	$ 8,612