Revenue and Contract Balances - Disaggregation of Revenue (Details) - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	Jun. 27, 2021	Jun. 28, 2020	Jun. 27, 2021	Jun. 28, 2020
Disaggregation of Revenue [Line Items]
Revenue	$ 801,633	$ 709,771	$ 2,321,500	$ 2,241,527
Fixed-price
Disaggregation of Revenue [Line Items]
Revenue	294,568	275,810	841,118	802,477
Time-and-materials
Disaggregation of Revenue [Line Items]
Revenue	379,705	309,123	1,082,143	1,047,900
Cost-plus
Disaggregation of Revenue [Line Items]
Revenue	127,360	124,838	398,239	391,150
U.S. state and local government
Disaggregation of Revenue [Line Items]
Revenue	135,717	97,163	390,464	324,670
U.S. federal government
Disaggregation of Revenue [Line Items]
Revenue	265,999	243,414	799,560	731,977
U.S. commercial
Disaggregation of Revenue [Line Items]
Revenue	153,100	168,491	454,607	510,770
International
Disaggregation of Revenue [Line Items]
Revenue	$ 246,817	$ 200,703	$ 676,869	$ 674,110