Revenue and Contract Balances - Disaggregation of Revenue (Details) - USD ($) $ in Thousands	3 Months Ended								12 Months Ended
	Oct. 01, 2023	Jul. 02, 2023	Apr. 02, 2023	Jan. 01, 2023	Oct. 02, 2022	Jul. 03, 2022	Apr. 03, 2022	Jan. 02, 2022	Oct. 01, 2023	Oct. 02, 2022	Oct. 03, 2021
Disaggregation of Revenue [Line Items]
Revenue	$ 1,260,611	$ 1,208,947	$ 1,158,226	$ 894,766	$ 902,562	$ 890,231	$ 852,744	$ 858,510	$ 4,522,550	$ 3,504,048	$ 3,213,513
Fixed-price
Disaggregation of Revenue [Line Items]
Revenue									1,643,849	1,317,993	1,191,244
Time-and-materials
Disaggregation of Revenue [Line Items]
Revenue									2,166,671	1,637,019	1,492,813
Cost-plus
Disaggregation of Revenue [Line Items]
Revenue									712,030	549,036	529,456
U.S. federal government
Disaggregation of Revenue [Line Items]
Revenue									1,387,101	1,064,347	1,081,608
U.S. state and local government
Disaggregation of Revenue [Line Items]
Revenue									607,074	603,286	536,309
U.S. commercial
Disaggregation of Revenue [Line Items]
Revenue									869,460	748,953	638,169
International
Disaggregation of Revenue [Line Items]
Revenue									$ 1,658,915	$ 1,087,462	$ 957,427