Revenue and Contract Balances - Disaggregation of Revenue (Details) - USD ($) $ in Thousands	3 Months Ended
	Jan. 01, 2023	Jan. 02, 2022
Disaggregation of Revenue [Line Items]
Revenue	$ 894,766	$ 858,510
Fixed-price
Disaggregation of Revenue [Line Items]
Revenue	327,737	331,248
Time-and-materials
Disaggregation of Revenue [Line Items]
Revenue	420,570	395,648
Cost-plus
Disaggregation of Revenue [Line Items]
Revenue	146,459	131,614
U.S. federal government
Disaggregation of Revenue [Line Items]
Revenue	276,075	266,797
U.S. state and local government
Disaggregation of Revenue [Line Items]
Revenue	153,195	159,008
U.S. commercial
Disaggregation of Revenue [Line Items]
Revenue	198,956	176,904
International
Disaggregation of Revenue [Line Items]
Revenue	$ 266,540	$ 255,801