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Share-based Payments (Details) - USD ($)
$ / shares in Units, shares in Millions, $ in Millions
 6 Months Ended 12 Months Ended
Mar. 31, 2018
Mar. 31, 2017
Sep. 30, 2017
Stock options, Weighted average exercise price      
Vesting period 3 years   3 years
Recognized compensation expense $ 37.2 $ 38.1  
Unrecognized compensation expense $ 133.5   $ 96.8
Employee Stock Option      
Shares of stock under options      
Balance at the beginning of the period (in shares) 0.7 0.9 0.9
Options exercised (in shares) (0.1) (0.2)  
Balance at the end of the period (in shares) 0.6 0.7 0.7
Vested and expected to vest in the future at the end of the period (in shares) 0.6 0.7  
Stock options, Weighted average exercise price      
Balance at the beginning of the period (in dollars per share) $ 31.11 $ 30.36 $ 30.36
Options exercised (in dollars per share) 27.79 26.42  
Balance at the end of the period (in dollars per share) 31.62 31.11 $ 31.11
Vested and expected to vest in the future at the end of the period (in dollars per share) $ 31.62 31.11  
Performance Earnings Program      
Stock options, Weighted average exercise price      
Vesting period 3 years    
Weighted average grant-date fair value of stock options granted (in dollars per share) $ 37.69 38.16  
Restricted Stock Units (RSUs)      
Stock options, Weighted average exercise price      
Weighted average grant-date fair value of stock options granted (in dollars per share) $ 36.91 $ 38.05