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Stock-based Compensation (Narrative) (Details) - USD ($)
$ / shares in Units, shares in Thousands, $ in Millions
3 Months Ended 12 Months Ended
Oct. 31, 2021
Nov. 01, 2020
Oct. 27, 2019
Oct. 28, 2018
Aug. 01, 2021
Aug. 02, 2020
Jul. 28, 2019
Stock-based Compensation              
Excess Tax Benefit/(Deficiency) from Share-based Compensation, Operating Activities         $ 1 $ 1 $ (6)
Cash received from the exercise of stock options         2 23 0
Share-based Compensation Arrangement by Share-based Payment Award, Options, Exercises in Period, Intrinsic Value         $ 0 $ 2 $ 0
EPS Performance Restricted Stock Units [Member]              
Stock-based Compensation              
Share-based Compensation Arrangement by Share-based Payment Award, Award Vesting Period         3 years    
Strategic Performance Restricted Stock Units [Member]              
Stock-based Compensation              
Share-based Compensation Arrangement by Share-based Payment Award, Award Vesting Period         3 years    
FCF Performance Restricted Stock Units [Member]              
Stock-based Compensation              
Share-based Compensation Arrangement by Share-based Payment Award, Award Vesting Period         3 years    
Nonvested, Units         239    
Nonvested, Weighted-Average Grant-Date Fair Value         $ 44.10    
Share Based Compensation Arrangements By Share Based Payment Award Equity Instruments Other than Options Issued in Period             388
Time Lapse Restricted Stock Units [Member]              
Stock-based Compensation              
Share-based Compensation Arrangement by Share-based Payment Award, Award Vesting Period         3 years    
Share-based Payment Arrangement, Option [Member]              
Stock-based Compensation              
Share-based Compensation Arrangement by Share-based Payment Award, Award Vesting Period         3 years    
Share-based Compensation Arrangement by Share-based Payment Award, Expiration Period         10 years    
Time Lapse, EPS Performance, And FCF Performance Restricted Stock Units [Member]              
Stock-based Compensation              
Remaining unearned compensation on nonvested awards         $ 30    
Weighted-average remaining service period, years         1 year 7 months 6 days    
Nonvested, Units         1,814 1,866  
Nonvested, Weighted-Average Grant-Date Fair Value         $ 45.63 $ 43.18  
Fair value of restricted units and shares vested         $ 38 $ 41 $ 26
Granted, Weighted-Average Grant-Date Fair Value         $ 48.37 $ 46.82 $ 36.51
TSR Performance Restricted Stock/Units [Member]              
Stock-based Compensation              
Share-based Compensation Arrangement by Share-based Payment Award, Award Vesting Period         3 years    
Remaining unearned compensation on nonvested awards         $ 25    
Weighted-average remaining service period, years         1 year 7 months 6 days    
Nonvested, Units         1,222 1,254  
Nonvested, Weighted-Average Grant-Date Fair Value         $ 53.60 $ 47.83  
Fair value of restricted units and shares vested         $ 11    
Granted, Weighted-Average Grant-Date Fair Value         $ 54.93 $ 63.06 $ 31.29
Share-based Compensation Arrangement by Share-based Payment Award, Award Vesting Rights, Percentage   50.00% 0.00% 0.00%      
Minimum [Member] | EPS Performance Restricted Stock Units [Member]              
Stock-based Compensation              
Share-based Compensation Arrangement by Share-based Payment Award, Award Vesting Rights, Percentage         0.00%    
Minimum [Member] | Strategic Performance Restricted Stock Units [Member]              
Stock-based Compensation              
Share-based Compensation Arrangement by Share-based Payment Award, Award Vesting Rights, Percentage         0.00%    
Minimum [Member] | FCF Performance Restricted Stock Units [Member]              
Stock-based Compensation              
Share-based Compensation Arrangement by Share-based Payment Award, Award Vesting Rights, Percentage         0.00%    
Minimum [Member] | TSR Performance Restricted Stock/Units [Member]              
Stock-based Compensation              
Share-based Compensation Arrangement by Share-based Payment Award, Award Vesting Rights, Percentage         0.00%    
Maximum [Member] | EPS Performance Restricted Stock Units [Member]              
Stock-based Compensation              
Share-based Compensation Arrangement by Share-based Payment Award, Award Vesting Rights, Percentage         100.00%    
Maximum [Member] | Strategic Performance Restricted Stock Units [Member]              
Stock-based Compensation              
Share-based Compensation Arrangement by Share-based Payment Award, Award Vesting Rights, Percentage         200.00%    
Maximum [Member] | FCF Performance Restricted Stock Units [Member]              
Stock-based Compensation              
Share-based Compensation Arrangement by Share-based Payment Award, Award Vesting Rights, Percentage         200.00%    
Maximum [Member] | Share-based Payment Arrangement, Option [Member]              
Stock-based Compensation              
Remaining unearned compensation on nonvested awards         $ 1    
Weighted-average remaining service period, years         1 year    
Maximum [Member] | TSR Performance Restricted Stock/Units [Member]              
Stock-based Compensation              
Share-based Compensation Arrangement by Share-based Payment Award, Award Vesting Rights, Percentage         200.00%    
2005 Long Term Incentive Plan [Member]              
Stock-based Compensation              
Share-based Compensation Arrangement by Share-based Payment Award, Number of Shares Authorized         6,000    
2005 Long Term Incentive Plan, Total Shares Authorized, as Amended In 2008 [Member]              
Stock-based Compensation              
Share-based Compensation Arrangement by Share-based Payment Award, Number of Shares Authorized         10,500    
2005 Long Term Incentive Plan, Total Shares Authorized, as Amended in 2010 [Member]              
Stock-based Compensation              
Share-based Compensation Arrangement by Share-based Payment Award, Number of Shares Authorized         17,500    
2015 Long-Term Incentive Plan [Member]              
Stock-based Compensation              
Share-based Compensation Arrangement by Share-based Payment Award, Number of Shares Authorized         13,000    
2005 Long-Term Incentive Plan Rolled into the 2015 Long-Term Incentive Plan              
Stock-based Compensation              
Share-based Compensation Arrangement by Share-based Payment Award, Number of Shares Authorized         6,000    
Forecast [Member] | FCF Performance Restricted Stock Units [Member]              
Stock-based Compensation              
Share-based Compensation Arrangement by Share-based Payment Award, Award Vesting Rights, Percentage 167.00%            
Forecast [Member] | TSR Performance Restricted Stock/Units [Member]              
Stock-based Compensation              
Share-based Compensation Arrangement by Share-based Payment Award, Award Vesting Rights, Percentage 75.00%