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Accumulated Other Comprehensive Loss (Details) - USD ($) $ in Thousands	12 Months Ended
	Mar. 31, 2022	Mar. 31, 2021	Mar. 31, 2020	Mar. 31, 2019
Accumulated Other Comprehensive Income (Loss) [Line Items]
Components of Accumulated Other Comprehensive Loss	$ 1,577,611	$ 1,358,298	$ 1,170,971	$ 1,095,831
Other comprehensive income (loss), cash flow hedge, gain (loss), reclassification, tax	0	543
Other comprehensive income (loss), defined benefit plan, gain (loss) arising during period, tax	(350)	(276)
Accumulated other comprehensive loss, net of tax
Accumulated Other Comprehensive Income (Loss) [Line Items]
Components of Accumulated Other Comprehensive Loss	(19,032)	(19,801)	$ (44,161)	$ (25,747)
Cumulative translation adjustment
Accumulated Other Comprehensive Income (Loss) [Line Items]
Components of Accumulated Other Comprehensive Loss	(20,204)	(18,908)
Unrealized loss on interest rate swaps, net of tax of $0 and $543, respectively
Accumulated Other Comprehensive Income (Loss) [Line Items]
Components of Accumulated Other Comprehensive Loss	0	(1,819)
Unrecognized net gain (loss) on pension plans, net of tax of $(350) and $(276), respectively
Accumulated Other Comprehensive Income (Loss) [Line Items]
Components of Accumulated Other Comprehensive Loss	$ 1,172	$ 926

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Amount of tax expense (benefit) for (increase) decrease in value of benefit obligation for change in actuarial assumptions and increase (decrease) in value of plan assets from experience different from that assumed of defined benefit plan, that has not been recognized in net periodic benefit (cost) credit.

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Amount of tax expense (benefit) for reclassification of gain (loss) from accumulated other comprehensive income (AOCI) for derivative instrument designated and qualifying as cash flow hedge included in assessment of hedge effectiveness.

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Total of all stockholders' equity (deficit) items, net of receivables from officers, directors, owners, and affiliates of the entity which are attributable to the parent. The amount of the economic entity's stockholders' equity attributable to the parent excludes the amount of stockholders' equity which is allocable to that ownership interest in subsidiary equity which is not attributable to the parent (noncontrolling interest, minority interest). This excludes temporary equity and is sometimes called permanent equity.

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