Revenue and Contract Balances - Disaggregation of Revenue (Details) - USD ($) $ in Thousands	3 Months Ended								12 Months Ended
	Oct. 02, 2022	Jul. 03, 2022	Apr. 03, 2022	Jan. 02, 2022	Oct. 03, 2021	Jun. 27, 2021	Mar. 28, 2021	Dec. 27, 2020	Oct. 02, 2022	Oct. 03, 2021	Sep. 27, 2020
Disaggregation of Revenue [Line Items]
Revenue	$ 902,562	$ 890,231	$ 852,744	$ 858,510	$ 892,012	$ 801,633	$ 754,764	$ 765,104	$ 3,504,048	$ 3,213,513	$ 2,994,891
Fixed-price
Disaggregation of Revenue [Line Items]
Revenue									1,317,993	1,191,244	1,078,432
Time-and-materials
Disaggregation of Revenue [Line Items]
Revenue									1,637,019	1,492,813	1,391,592
Cost-plus
Disaggregation of Revenue [Line Items]
Revenue									549,036	529,456	524,867
U.S. federal government
Disaggregation of Revenue [Line Items]
Revenue									1,064,347	1,081,608	993,835
U.S. state and local government
Disaggregation of Revenue [Line Items]
Revenue									603,286	536,309	439,019
U.S. commercial
Disaggregation of Revenue [Line Items]
Revenue									748,953	638,169	674,605
International
Disaggregation of Revenue [Line Items]
Revenue									$ 1,087,462	$ 957,427	$ 887,432