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Share-Based Compensation - Equity Incentive Plans, RSU outstanding (Details) - USD ($)
$ / shares in Units, $ in Millions
12 Months Ended
Mar. 31, 2021
Mar. 31, 2020
Mar. 31, 2019
May 29, 2018
Weighted Average Grant Date Fair Value        
Share price (in dollars per share) $ 155.22      
Unvested share-based payment awards $ 300.1     $ 121.5
Restricted stock units' weighted average remaining expense recognition period (in years) 1 year 10 months 2 days      
Restricted Stock Units        
Number of Shares        
Nonvested shares at beginning of period (in shares) 5,742,053 6,291,962 5,672,440  
Granted (in shares) 2,339,247 2,182,044 1,951,408  
Assumed upon acquisition (in shares)     1,805,680  
Forfeited (in shares) (257,055) (340,659) (408,242)  
Vested (in shares) (1,882,336) (2,391,294) (2,729,324)  
Nonvested shares at end of period (in shares) 5,941,909 5,742,053 6,291,962  
Weighted Average Grant Date Fair Value        
Nonvested shares at beginning of period (in dollars per share) $ 76.11 $ 64.81 $ 50.79  
Granted (in dollars per share) 101.37 88.17 77.83  
Assumed upon acquisition (in dollars per share)     91.70  
Forfeited (in dollars per share) 83.37 75.50 73.36  
Vested (in dollars per share) 64.13 57.47 61.51  
Nonvested shares at end of period (in dollars per share) $ 89.54 $ 76.11 $ 64.81  
RSU Vested aggregate intrinsic value $ 218.5 $ 223.9 $ 229.3  
Total intrinsic value of RSU's outstanding $ 922.3