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Share-Based Compensation Share-Based Compensation (Details) - USD ($)
$ / shares in Units, $ in Thousands
 6 Months Ended
Sep. 30, 2024
Sep. 30, 2023
Share-based Compensation Arrangement by Share-based Payment Award [Line Item]    
Remaining shares available for grant 2,020,289  
Weighted-average assumptions used for options granted:    
Risk-free interest rate 4.21% 3.59%
Expected life of options 6 years 1 month 6 days 6 years
Exptected dividend yield of stock 0.94% 1.08%
Expected volatility of stock 28.42% 27.92%
Estimated forfeiture rate 2.07% 2.22%
Summary of share option activity:    
Outstanding at the beginning of the period 1,869,871  
Granted 217,426  
Exercised (188,205)  
Forfeited (7,008)  
Canceled (512)  
Outstanding at the end of the period 1,891,572  
Exercisable at the end of the period 1,322,218  
Weighted average exercise price:    
Outstanding at March 31, 2023 $ 168.22  
Granted 250.76  
Exercised 106.95  
Forfeited 237.49  
Canceled 250.06  
Outstanding at June 30, 2023 183.52  
Exercisable at June 30, 2023 $ 160.66  
Average Remaining Contractual Term, Outstanding at the end of the period 6 years 2 months 12 days  
Aggregate Intrinsic Value, Outstanding at the end of the period $ 115,080  
Average Remaining Contractual Term, Exercisable at the end of the period 5 years 1 month 6 days  
Aggregate Intrinsic Value, Exercisable at the end of the period $ 109,084  
Non-vested stock options outstanding expected to vest 556,678  
Ordinary shares, closing price $ 242.54  
Total intrinsic value of stock options exercised $ 24,446 $ 6,467
Net cash proceeds from the exercise of stock options $ 19,092 $ 2,740
Weighted average grant date fair value of stock option grants, per share $ 67.81 $ 54.60
Summary of non-vested restricted share activity:    
Unrecognized compensation cost related to nonvested share-based compensation granted $ 75,899  
Weighted Average Period For Total Compensation Expense Not Yet Recognized 1 year 8 months 12 days  
Restricted Stock    
Summary of non-vested restricted share activity:    
Number of Restricted Shares, Non-vested at Beginning of Period 463,381  
Weighted-Average Grant Date Fair Value, Non-vested at Beginning of Period $ 200.04  
Number of Restricted Shares, Granted 156,202  
Weighted-Average Grant Date Fair Value, Granted $ 228.77  
Number of Restricted Shares, Vested (127,532)  
Weighted-Average Grant Date Fair Value, Vested $ 185.66  
Number of Restricted Shares, Canceled (30,490)  
Weighted-Average Grant Date Fair Value, Canceled $ 206.80  
Number of Restricted Shares, Non-vested at End of Period 461,561  
Weighted-Average Grant Date Fair Value, Non-vested at End of Period $ 213.79  
Fair Value, Share-based Payment Awards, Other than Options $ 25,968  
Restricted Stock Units (RSUs)    
Summary of non-vested restricted share activity:    
Number of Restricted Shares, Non-vested at Beginning of Period 28,348  
Number of Restricted Shares, Granted 16,367  
Number of Restricted Shares, Vested (11,424)  
Number of Restricted Shares, Canceled (1,573)  
Number of Restricted Shares, Non-vested at End of Period 31,718