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Share-Based Compensation (Details) - USD ($)
$ / shares in Units, $ in Thousands
 12 Months Ended
Mar. 31, 2019
Mar. 31, 2018
Mar. 31, 2017
Share-based Compensation Arrangement by Share-based Payment Award [Line Item]      
Remaining shares available for grant 4,400,306    
Weighted-average assumptions used for options granted:      
Risk-free interest rate 2.64% 2.01% 1.29%
Expected life of options 6 years 2 months 12 days 5 years 8 months 12 days 5 years 8 months 12 days
Exptected dividend yield of stock 1.47% 1.58% 1.54%
Expected volatility of stock 19.91% 22.08% 22.92%
Estimated forfeiture rate 2.37% 2.25% 1.85%
Summary of share option activity:      
Number of Options, Outstanding, Beginning of Period 2,021,662    
Weighted Average Exercise Price, Outstanding, Beginning of Period $ 58.56    
Number of Options, Granted 436,121    
Weighted Average Exercise Price, Granted $ 114.49    
Number of Options, Exercised (335,358)    
Weighted Average Exercise Price, Exercised $ 40.70    
Number of Options, Forfeited (17,740)    
Weighted Average Exercise Price, Forfeited $ 79.91    
Number of Options, Outstanding, End of Period 2,104,685 2,021,662  
Weighted Average Exercise Price, Outstanding, End of Period $ 72.82 $ 58.56  
Average Remaining Contractual Term, Outstanding 6 years 8 months 12 days    
Aggregate Intrinsic Value, Outstanding $ 116,199    
Number of Options, Exercisable 1,164,583    
Weighted Average Exercise Price, Exercisable $ 57.81    
Share-based Compensation Arrangement by Share-based Payment Award, Options, Exercisable, Weighted Average Remaining Contractual Term 5 years 6 months    
Aggregate Intrinsic Value, Exercisable $ 81,780    
Non-vested stock options outstanding expected to vest 924,224    
Common Stock, Fair Market Value Per Share $ 128.03    
Total intrinsic value of stock options exercised $ 25,371 $ 16,096 $ 6,454
Net cash proceeds from the exercise of stock options 13,308 11,093 4,955
Tax benefit from stock option exercises $ 8,306 $ 6,581 $ 5,058
Weighted average grant date fair value of stock option grants, per share $ 18.12 $ 15.51 $ 13.42
Summary of non-vested restricted share activity:      
Number of Restricted Shares, Non-vested at Beginning of Period 35,431    
Number of Restricted Shares, Granted 22,038    
Number of Restricted Shares, Vested (23,290)    
Number of Restricted Shares, Canceled (960)    
Number of Restricted Shares, Non-vested at End of Period 33,219 35,431  
Unrecognized compensation cost related to nonvested share-based compensation granted $ 39,023    
Weighted average period for recognition of unrecognized compensation cost 2 years 1 month 2 days    
Stock Appreciation Rights (SARs)      
Summary of non-vested restricted share activity:      
FairValueOfOutstandingStockAppreciationRights $ 889 $ 1,437 $ 1,622
Restricted Stock      
Summary of non-vested restricted share activity:      
Number of Restricted Shares, Non-vested at Beginning of Period 763,201    
Weighted-Average Grant Date Fair Value, Non-vested at Beginning of Period $ 68.65    
Number of Restricted Shares, Granted 178,142    
Weighted-Average Grant Date Fair Value, Granted $ 104.83    
Number of Restricted Shares, Vested (233,629)    
Weighted-Average Grant Date Fair Value, Vested $ 62.15    
Number of Restricted Shares, Canceled (31,341)    
Weighted-Average Grant Date Fair Value, Canceled $ 76.98    
Number of Restricted Shares, Non-vested at End of Period 676,373 763,201  
Weighted-Average Grant Date Fair Value, Non-vested at End of Period $ 80.86 $ 68.65  
Fair Value, Share-based Payment Awards, Other than Options $ 15,968