Revenue and Contract Balances - Disaggregation of Revenue (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Apr. 03, 2022	Mar. 28, 2021	Apr. 03, 2022	Mar. 28, 2021
Disaggregation of Revenue [Line Items]
Revenue	$ 852,744	$ 754,764	$ 1,711,255	$ 1,519,868
Fixed-price
Disaggregation of Revenue [Line Items]
Revenue	316,304	272,118	647,552	546,551
Time-and-materials
Disaggregation of Revenue [Line Items]
Revenue	408,051	347,197	803,700	702,438
Cost-plus
Disaggregation of Revenue [Line Items]
Revenue	128,389	135,449	260,003	270,879
U.S. state and local government
Disaggregation of Revenue [Line Items]
Revenue	156,032	129,781	315,040	254,747
U.S. federal government
Disaggregation of Revenue [Line Items]
Revenue	253,272	267,696	520,069	533,561
U.S. commercial
Disaggregation of Revenue [Line Items]
Revenue	171,741	143,702	348,646	301,508
International
Disaggregation of Revenue [Line Items]
Revenue	$ 271,699	$ 213,585	$ 527,500	$ 430,052