Revenue and Contract Balances - Narrative (Details) - USD ($) $ in Thousands	12 Months Ended
	Oct. 02, 2022	Oct. 03, 2021
Disaggregation of Revenue [Line Items]
Contract liability revenue recognized during the period	$ 125,000	$ 119,000
Liabilities for anticipated losses	10,000	12,700
Estimated cost to complete the related contracts	$ 80,000	104,000
Period for billing and collecting unbilled receivables	12 months
Unbilled accounts receivable related to claims and requests for equitable adjustment on contracts	$ 0	11,000
Remaining unsatisfied performance obligation	$ 3,721,634
Remaining performance obligation, termination notice period one	30 days
Remaining performance obligation, termination notice period two	60 years
Remaining performance obligation, termination notice period three	90 days
CIG
Disaggregation of Revenue [Line Items]
Gains (losses) due to change in contract value		$ 2,800