Revenue and Contract Balances - Disaggregation of Revenue (Details) - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	Jul. 03, 2022	Jun. 27, 2021	Jul. 03, 2022	Jun. 27, 2021
Disaggregation of Revenue [Line Items]
Revenue	$ 890,231	$ 801,633	$ 2,601,485	$ 2,321,500
Fixed-price
Disaggregation of Revenue [Line Items]
Revenue	335,014	294,568	982,565	841,118
Time-and-materials
Disaggregation of Revenue [Line Items]
Revenue	417,898	379,705	1,221,598	1,082,143
Cost-plus
Disaggregation of Revenue [Line Items]
Revenue	137,319	127,360	397,322	398,239
U.S. state and local government
Disaggregation of Revenue [Line Items]
Revenue	150,731	135,717	465,770	390,464
U.S. federal government
Disaggregation of Revenue [Line Items]
Revenue	261,434	265,999	781,503	799,560
U.S. commercial
Disaggregation of Revenue [Line Items]
Revenue	188,255	153,100	536,901	454,607
International
Disaggregation of Revenue [Line Items]
Revenue	$ 289,811	$ 246,817	$ 817,311	$ 676,869