Revenue Recognition - Disaggregation of Revenue (Details) - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	Jun. 30, 2019	Jul. 01, 2018	Jun. 30, 2019	Jul. 01, 2018
Disaggregation of Revenue [Line Items]
Revenue	$ 825,793	$ 764,795	$ 2,265,846	$ 2,224,805
U.S. state and local government
Disaggregation of Revenue [Line Items]
Revenue	172,148	103,169	425,296	359,828
U.S. federal government
Disaggregation of Revenue [Line Items]
Revenue	245,723	245,982	686,979	719,181
U.S. commercial
Disaggregation of Revenue [Line Items]
Revenue	194,980	208,507	533,738	595,691
International
Disaggregation of Revenue [Line Items]
Revenue	212,942	207,137	619,833	550,105
Fixed-price
Disaggregation of Revenue [Line Items]
Revenue	271,287	270,565	760,051	730,863
Time-and-materials
Disaggregation of Revenue [Line Items]
Revenue	419,564	351,436	1,101,728	1,061,798
Cost-plus
Disaggregation of Revenue [Line Items]
Revenue	$ 134,942	$ 142,794	$ 404,067	$ 432,144