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Accumulated Other Comprehensive Loss (Details) - USD ($)
$ in Thousands
12 Months Ended
Mar. 31, 2023
Mar. 31, 2022
Mar. 31, 2021
Mar. 31, 2020
Accumulated Other Comprehensive Income (Loss) [Line Items]        
Components of Accumulated Other Comprehensive Loss $ 1,447,084 $ 1,577,611 $ 1,358,298 $ 1,170,971
Other comprehensive income (loss), defined benefit plan, gain (loss) arising during period, tax (214) (350)    
Accumulated other comprehensive loss, net of tax        
Accumulated Other Comprehensive Income (Loss) [Line Items]        
Components of Accumulated Other Comprehensive Loss (31,564) (19,032) $ (19,801) $ (44,161)
Cumulative translation adjustment        
Accumulated Other Comprehensive Income (Loss) [Line Items]        
Components of Accumulated Other Comprehensive Loss (32,280) (20,204)    
Unrecognized net gain on pension plans, net of tax of $(214) and $(350), respectively        
Accumulated Other Comprehensive Income (Loss) [Line Items]        
Components of Accumulated Other Comprehensive Loss $ 716 $ 1,172