Revenue and Contract Balances - Narrative (Details) - USD ($)	3 Months Ended
	Jan. 01, 2023	Jan. 02, 2022	Oct. 02, 2022
Disaggregation of Revenue [Line Items]
Contract liability revenue recognized during the period	$ 81,000,000	$ 63,000,000
Net favorable (unfavorable) revenue and operating income adjustments	3,500,000	2,800,000
Liabilities for anticipated losses	7,600,000		$ 10,000,000
Estimated cost to complete the related contracts	$ 55,000,000		80,000,000
Period for billing and collecting unbilled receivables	12 months
Remaining unsatisfied performance obligation	$ 3,790,120,000
Remaining performance obligation, termination notice period one	30 days
Remaining performance obligation, termination notice period two	60 days
Remaining performance obligation, termination notice period three	90 days
Remediation and Construction Management
Disaggregation of Revenue [Line Items]
Accounts receivable related to claims and requests for equitable adjustment on contracts			$ 0
CIG
Disaggregation of Revenue [Line Items]
Net favorable (unfavorable) revenue and operating income adjustments	$ 0	$ 0