Revenue and Contract Balances - Narrative (Details) - USD ($) $ in Thousands	12 Months Ended
	Oct. 03, 2021	Sep. 27, 2020
Disaggregation of Revenue [Line Items]
Contract liability revenue recognized during the period	$ 119,000	$ 118,000
Net favorable operating income adjustments	700	800
Liabilities for anticipated losses	12,700	13,200
Estimated cost to complete the related contracts	$ 104,000	118,000
Period for billing and collecting unbilled receivables	12 months
Unbilled accounts receivable related to claims and requests for equitable adjustment on contracts	$ 11,000	14,000
Remaining unsatisfied performance obligation	$ 3,467,833
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	$ (4,400)	$ 2,800