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Stock Compensation (Maximum Future Value of Performance Shares) (Details) (USD $)
In Millions, except Share data, unless otherwise specified
12 Months Ended
Jan. 03, 2015
Dec. 28, 2013
Dec. 29, 2012
Feb. 22, 2014
Stock Compensation [Abstract]        
2014 Award $ 29k_MaximumFutureValueOfPerformanceSharesTwoThousandFourteen      
2013 Award   25k_MaximumFutureValueOfPerformanceSharesTwoThousandThirteen    
2012 Award     23k_MaximumFutureValueOfPerformanceSharesTwoThousandTwelve  
Performance share based awards cumulative target period, in years 3 years      
Number of shares that correspond with target grants 223,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod 194,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod 178,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod  
Grant-date fair value of shares that correspond with target grants $ 54us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue $ 54us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue $ 47us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue  
Number of performance shares that could be issued on the vesting date, minimum 0.00%k_PerformanceSharesIssuedOnVestingDateMinimum      
Number of performance shares that could be issued on the vesting date, maximum 200.00%k_PerformanceSharesIssuedOnVestingDateMaximum      
2011 Performance share award settlement in terms of original target       60.00%k_PerformanceAwardSettlementStockIssuedAsPercentageOfOriginalTarget
2011 Performance share award settlement in dollars       $ 3us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsTotalShareBasedLiabilitiesPaid