Revenue and Contract Balances - Disaggregation of Revenue (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Mar. 31, 2024	Apr. 02, 2023	Mar. 31, 2024	Apr. 02, 2023
Disaggregation of Revenue [Line Items]
Revenue	$ 1,251,616	$ 1,158,226	$ 2,479,883	$ 2,052,991
Fixed-price
Disaggregation of Revenue [Line Items]
Revenue	459,022	413,924	930,464	741,661
Time-and-materials
Disaggregation of Revenue [Line Items]
Revenue	591,844	533,496	1,141,495	954,066
Cost-plus
Disaggregation of Revenue [Line Items]
Revenue	200,750	210,806	407,924	357,264
U.S. federal government
Disaggregation of Revenue [Line Items]
Revenue	407,002	382,374	789,078	658,449
U.S. state and local government
Disaggregation of Revenue [Line Items]
Revenue	147,551	147,791	298,476	300,985
U.S. commercial
Disaggregation of Revenue [Line Items]
Revenue	201,407	208,538	423,837	407,494
International
Disaggregation of Revenue [Line Items]
Revenue	$ 495,656	$ 419,523	$ 968,492	$ 686,063