Income Taxes - Income Tax Expense (Details) - USD ($) $ in Thousands	12 Months Ended
	Mar. 31, 2020	Mar. 31, 2019	Mar. 31, 2018
Income (Loss) Before Income Taxes [Abstract]
Domestic	$ 206,111	$ 181,730	$ 71,482
Foreign	134,755	147,204	149,214
Income before income taxes	340,866	328,934	220,696
Intercompany dividends	150,000	130,000	250,000
Current
Federal	47,087	33,334	80,339
State	635	9,084	3,437
Foreign	14,068	15,269	14,388
Total	61,790	57,687	98,164
Deferred
Federal	4,626	6,612	12,007
State	(462)	2,236	391
Foreign	(1,230)	(1,909)	(4,260)
Total	2,934	6,939	8,138
Total	64,724	64,626	106,302
Actual income taxes differed from that obtained by applying the statutory federal income tax rate to income before income taxes
Computed expected income taxes	71,582	69,076	69,556
State income taxes, net of federal income tax benefit	11,042	9,329	9,044
Foreign rate differential	(17,966)	(20,105)	(37,090)
Unrecognized tax benefits	6,695	786	1,301
Return to provision adjustments	(1,682)	(179)	(2,252)
Nontaxable income	(4,584)	(4,257)	(7,006)
Nondeductible expense	4,162	7,742	1,382
US tax on deemed repatriated foreign earnings	2,343	5,848	57,138
Re-measurement of deferred taxes	0	(983)	14,395
Tax audit settlements	(3,956)	0	0
Statutory foreign income tax expense (benefit)	(906)	276	59
Other	(2,006)	(2,907)	(225)
Total	$ 64,724	64,626	106,302
Income Tax Contingency [Line Items]
Provisional transition tax			59,114
Transition tax		$ 57,895
State Tax Authority
Income Tax Contingency [Line Items]
Provisional transition tax			$ 1,976