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Stockholders' Equity - Repurchase Programs (Details) - USD ($)
12 Months Ended
Mar. 31, 2020
Mar. 31, 2019
Mar. 31, 2018
Jan. 31, 2019
Class of Stock [Line Items]        
Dollar value of shares that may yet be repurchased $ 159,807,000      
Total number of shares repurchased (in shares) 1,296,201 1,400,699 1,702,653  
Average price paid per share (in dollars per share) $ 146.89 $ 115.22 $ 87.91  
Dollar value of shares repurchased $ 190,405,000 $ 161,395,000 $ 149,687,000  
Stock Repurchase Programs        
Class of Stock [Line Items]        
Authorized amount of shares to repurchase       $ 796,000,000