Revenue and Contract Balances - Disaggregation of Revenue (Details) - USD ($) $ in Thousands	3 Months Ended								12 Months Ended
	Sep. 29, 2024	Jun. 30, 2024	Mar. 31, 2024	Dec. 31, 2023	Oct. 01, 2023	Jul. 02, 2023	Apr. 02, 2023	Jan. 01, 2023	Sep. 29, 2024	Oct. 01, 2023	Oct. 02, 2022
Disaggregation of Revenue [Line Items]
Revenue	$ 1,374,473	$ 1,344,323	$ 1,251,616	$ 1,228,267	$ 1,260,611	$ 1,208,947	$ 1,158,226	$ 894,766	$ 5,198,679	$ 4,522,550	$ 3,504,048
Fixed-price
Disaggregation of Revenue [Line Items]
Revenue									2,016,638	1,643,849	1,317,993
Time-and-materials
Disaggregation of Revenue [Line Items]
Revenue									2,337,913	2,166,671	1,637,019
Cost-plus
Disaggregation of Revenue [Line Items]
Revenue									844,128	712,030	549,036
U.S. federal government
Disaggregation of Revenue [Line Items]
Revenue									1,675,996	1,387,101	1,064,347
U.S. state and local government
Disaggregation of Revenue [Line Items]
Revenue									613,185	607,074	603,286
U.S. commercial
Disaggregation of Revenue [Line Items]
Revenue									909,642	869,460	748,953
International
Disaggregation of Revenue [Line Items]
Revenue									$ 1,999,856	$ 1,658,915	$ 1,087,462