Revenue and Contract Balances - Disaggregation of Revenue (Details) - USD ($) $ in Thousands	3 Months Ended								12 Months Ended
	Oct. 03, 2021	Jun. 27, 2021	Mar. 28, 2021	Dec. 27, 2020	Sep. 27, 2020	Jun. 28, 2020	Mar. 29, 2020	Dec. 29, 2019	Oct. 03, 2021	Sep. 27, 2020	Sep. 29, 2019
Disaggregation of Revenue [Line Items]
Revenue	$ 892,012	$ 801,633	$ 754,764	$ 765,104	$ 753,364	$ 709,771	$ 734,133	$ 797,623	$ 3,213,513	$ 2,994,891	$ 3,107,348
Fixed-price
Disaggregation of Revenue [Line Items]
Revenue									1,191,244	1,078,432	1,048,158
Time-and-materials
Disaggregation of Revenue [Line Items]
Revenue									1,492,813	1,391,592	1,509,900
Cost-plus
Disaggregation of Revenue [Line Items]
Revenue									529,456	524,867	549,290
U.S. state and local government
Disaggregation of Revenue [Line Items]
Revenue									536,309	439,019	587,364
U.S. federal government
Disaggregation of Revenue [Line Items]
Revenue									1,081,608	993,835	941,102
U.S. commercial
Disaggregation of Revenue [Line Items]
Revenue									638,169	674,605	719,314
International
Disaggregation of Revenue [Line Items]
Revenue									$ 957,427	$ 887,432	$ 859,568