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Shareholders' Equity (Accumulated Other Comprehensive Income (Loss)) (Details) - USD ($) $ in Thousands	12 Months Ended
	Mar. 31, 2019	Mar. 31, 2018	Mar. 31, 2017
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning of the period	$ 1,050,557	$ 856,111	$ 759,948
Other comprehensive income (loss)	(12,243)	7,251	11,279
End of the period balance	1,176,339	1,050,557	856,111
Cumulative Translation Adjustment
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning of the period	(83,848)
Other comprehensive income (loss)	(8,300)
End of the period balance	(92,148)	(83,848)
Defined Benefit Plan
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning of the period	(6,398)
Other comprehensive income (loss)	(7,534)
End of the period balance	(13,932)	(6,398)
Deferred Hedging Gains (Losses)
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning of the period	(3,209)
Other comprehensive income (loss)	3,591
End of the period balance	382	(3,209)
Accumulated other comprehensive loss
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Beginning of the period	(93,455)	(100,706)	(111,985)
End of the period balance	$ (105,698)	$ (93,455)	$ (100,706)