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Pension and Other Postretirement Benefit Plans (Narrative) (Details)
$ in Millions
 3 Months Ended 12 Months Ended
Dec. 29, 2018
plan
Oct. 01, 2022
USD ($)
plan
Oct. 02, 2021
USD ($)
Oct. 03, 2020
USD ($)
Apr. 03, 2021
USD ($)
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]          
Defined Contribution Plan, Cost   $ 114 $ 106 $ 103  
Pension Fund of Local 227          
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]          
Multiemployer Plans, Withdrawal Obligation   $ 1      
Hillshire Hourly and Salaried Plans          
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]          
Assets for Plan Benefits, Defined Benefit Plan         $ 52
Pension Plan [Member]          
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]          
Defined Benefit Plan, Gain from Providing Special and Contractual Termination Benefits       112  
Defined Benefit Plan, Number of Plans | plan   4      
Multiemployer Plan, Employer Contribution, Cost   $ 2 1    
Defined Benefit Plan, Expected Future Employer Contributions, Next Fiscal Year   13      
Defined Benefit Plan, Plan Assets, Contributions by Employer   $ 13 15 19  
Defined Benefit Plans with Accumulated Benefit Obligations in Excess of Plan Assets, Number of Plans | plan   3      
Pension Plan [Member] | Defined Benefit Plan, Funded Plan | Qualified Plan          
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]          
Defined Benefit Plan, Number of Frozen and Noncontributory Plans | plan   1      
Defined Benefit Plan, Plan Assets, Contributions by Employer   $ 1 1    
Defined Benefit Plan, Benefit Obligation   17 28 31  
Defined Benefit Plan, Expected Amortization, Next Fiscal Year   0      
Defined Benefit Plan, Accumulated Benefit Obligation   17 28    
Defined Benefit Plan, Number of Plans Subject to Settlement | plan 3        
Assets for Plan Benefits, Defined Benefit Plan   7 5    
Defined Benefit Plan, Plan Assets, Amount   $ 24 33 35  
Pension Plan [Member] | Defined Benefit Plan, Unfunded Plan | Nonqualified Plan          
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]          
Defined Benefit Plan, Number of Plans | plan   3      
Defined Benefit Plan, Plan Assets, Contributions by Employer   $ 13 14    
Defined Benefit Plan, Benefit Obligation   166 220 238  
Assets for Plan Benefits, Defined Benefit Plan   0 0    
Defined Benefit Plan, Plan Assets, Amount   $ 0 0 0  
Other Postretirement Benefits Plan [Member]          
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]          
Defined Benefit Plan, Number of Plans | plan   8      
Defined Benefit Plan, Plan Assets, Contributions by Employer   $ 4 3    
Defined Benefit Plan, Benefit Obligation   55 65 74  
Defined Benefit Plan, Gain from Plan Amendment     34    
Assets for Plan Benefits, Defined Benefit Plan   0 0    
Defined Benefit Plan, Plan Assets, Amount   $ 0 $ 0 $ 0  
Other Postretirement Benefits Plan [Member] | Other Postretirement Benefit Plans, Fixed Annual Payments or Life Insurance          
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]          
Defined Benefit Plan, Number of Plans | plan   2      
Defined Benefit Plan, Benefit Obligation   $ 10      
Postretirement Health Coverage          
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]          
Defined Benefit Plan, Number of Plans | plan   5      
Postretirement Health Coverage | Other Postretirement Benefit Plans, Fixed Annual Payments or Life Insurance          
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]          
Defined Benefit Plan, Number of Plans | plan   1      
Postretirement Health Coverage | Other Postretirement Benefit Plan, Hillshire and Keystone Plans          
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]          
Defined Benefit Plan, Number of Plans | plan   2      
Postretirement Health Coverage | Other Postretirement Benefit Plan, Heathcare Cost Trend Rates, Hillshire Plan          
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]          
Defined Benefit Plan, Benefit Obligation   $ 1      
Defined Benefit Plan, Health Care Cost Trend Rate Assumed, Next Fiscal Year   6.80%      
Defined Benefit Plan, Ultimate Health Care Cost Trend Rate   4.50%      
Postretirement Health Coverage | Other Postretirement Benefit Plan, Heathcare Cost Trend Rates, Keystone Plan          
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]          
Defined Benefit Plan, Benefit Obligation   $ 3      
Defined Benefit Plan, Health Care Cost Trend Rate Assumed, Next Fiscal Year   7.50%      
Defined Benefit Plan, Ultimate Health Care Cost Trend Rate   4.50%      
Postretirement Health Coverage | Other Postretirement Benefit Plan, Plan Amendments          
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]          
Defined Benefit Plan, Number of Plans | plan   1      
Postretirement Health Coverage | Other Postretirement Benefit Plan, Plan Amendments | Maximum          
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]          
Defined Benefit Plan, Benefit Obligation   $ 1      
Postretirement Life Insurance | Other Postretirement Benefit Plans, Fixed Annual Payments or Life Insurance          
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]          
Defined Benefit Plan, Number of Plans | plan   1