Revenue and Contract Balances - Disaggregation of Revenue (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Apr. 02, 2023	Apr. 03, 2022	Apr. 02, 2023	Apr. 03, 2022
Disaggregation of Revenue [Line Items]
Revenue	$ 1,158,226	$ 852,744	$ 2,052,991	$ 1,711,255
Fixed-price
Disaggregation of Revenue [Line Items]
Revenue	413,924	316,304	741,661	647,552
Time-and-materials
Disaggregation of Revenue [Line Items]
Revenue	533,496	408,051	954,066	803,700
Cost-plus
Disaggregation of Revenue [Line Items]
Revenue	210,806	128,389	357,264	260,003
U.S. federal government
Disaggregation of Revenue [Line Items]
Revenue	382,374	253,272	658,449	520,069
U.S. state and local government
Disaggregation of Revenue [Line Items]
Revenue	147,791	156,032	300,985	315,040
U.S. commercial
Disaggregation of Revenue [Line Items]
Revenue	208,538	171,741	407,494	348,646
International
Disaggregation of Revenue [Line Items]
Revenue	$ 419,523	$ 271,699	$ 686,063	$ 527,500