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Revenue and Contract Balances - Narrative (Details) - USD ($)
3 Months Ended 9 Months Ended
Jul. 03, 2022
Jun. 27, 2021
Jul. 03, 2022
Jun. 27, 2021
Oct. 03, 2021
Disaggregation of Revenue [Line Items]          
Contract liability revenue recognized during the period     $ 111,000,000 $ 108,000,000  
Net favorable (unfavorable) revenue and operating income adjustments $ (2,800,000) $ 1,700,000 2,200,000 2,800,000  
Liabilities for anticipated losses 11,100,000   11,100,000   $ 12,700,000
Estimated cost to complete the related contracts 84,000,000   $ 84,000,000   104,000,000
Period for billing and collecting unbilled receivables     12 months    
Remaining unsatisfied performance obligation 3,495,454,000   $ 3,495,454,000    
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    
RCM          
Disaggregation of Revenue [Line Items]          
Accounts receivable related to claims and requests for equitable adjustment on contracts $ 0   $ 0   $ 11,000,000
CIG          
Disaggregation of Revenue [Line Items]          
Net favorable (unfavorable) revenue and operating income adjustments     $ 0 $ 2,800,000