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Computation of Earnings Per Common Share - Narratives (Details) - $ / shares
6 Months Ended
Jan. 27, 2018
Jul. 29, 2017
Jul. 30, 2016
Sep. 15, 2015
Shares used in computing earnings per common share:        
Adoption of accounting principled effect on diluted shares 177,575      
Weighted average stock price (usd per share) $ 106.11      
Convertible Note Hedge        
Shares used in computing earnings per common share:        
Debt instrument, convertible, conversion price (per share) $ 96.89     $ 96.89
0.75% Convertible Senior Notes Due 2021        
Shares used in computing earnings per common share:        
Debt, interest rate (in percent) 0.75% 0.75% 0.75%  
Debt instrument, convertible, conversion price (per share)       96.89
Class of warrant or right, exercise price of warrants or rights (per warrant) $ 130.43     $ 130.43