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Share-Based Compensation - Restricted Stock Units (Details) - USD ($)
$ / shares in Units, $ in Millions
12 Months Ended
Mar. 31, 2020
Mar. 31, 2019
Mar. 31, 2018
Weighted Average Grant Date Fair Value      
Share price (in dollars per share) $ 67.80    
Total compensation cost not yet recognized $ 263.2    
Restricted stock units' weighted average remaining expense recognition period (in years) 2 years 10 days    
Restricted Stock Units      
Number of Shares      
Nonvested shares at beginning of period (in shares) 6,291,962 5,672,440 6,419,456
Granted (in shares) 2,182,044 1,951,408 1,267,536
Assumed upon acquisition (in shares)   1,805,680  
Forfeited (in shares) (340,659) (408,242) (279,051)
Vested (in shares) (2,391,294) (2,729,324) (1,735,501)
Nonvested shares at end of period (in shares) 5,742,053 6,291,962 5,672,440
Weighted Average Grant Date Fair Value      
Nonvested shares at beginning of period (in dollars per share) $ 64.81 $ 50.79 $ 42.06
Granted (in dollars per share) 88.17 77.83 77.26
Assumed upon acquisition (in dollars per share)   91.70  
Forfeited (in dollars per share) 75.50 73.36 49.65
Vested (in dollars per share) 57.47 61.51 38.00
Nonvested shares at end of period (in dollars per share) $ 76.11 $ 64.81 $ 50.79
Share-based compensation arrangement by share-based payment award, equity instruments other than options, aggregate intrinsic value, vested $ 223.9 $ 229.3 $ 146.0
Share-based compensation arrangement by share-based payment award, equity instruments other than options, aggregate intrinsic value, outstanding $ 389.3