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Stock-Based Compensation - Annual RSUs and Annual PSUs (Details) - Annual RSUs and Annual PSUs - Stock Incentive Plan 2015 - $ / shares
12 Months Ended
Mar. 31, 2020
Mar. 31, 2019
Mar. 31, 2018
Number of Shares      
Nonvested at the beginning of the period (in shares) 231,399 289,297 226,244
Granted (in shares) 67,515 94,063 187,554
Vested (in shares) (121,572) (118,903) (101,791)
Forfeited (in shares) (14,993) (33,058) (22,710)
Nonvested at the end of the period (in shares) 162,349 231,399 289,297
Weighted- Average Grant-Date Fair Value      
Outstanding at the beginning of the period (in dollars per share) $ 84.75 $ 65.18 $ 63.96
Granted (in dollars per share) 172.34 116.68 67.92
Vested (in dollars per share) (76.81) (64.39) (67.63)
Forfeited (in dollars per share) (113.49) (77.60) (64.59)
Outstanding at the end of the period (in dollars per share) $ 124.47 $ 84.75 $ 65.18