Income Taxes (Details) - USD ($) $ / shares in Units, $ in Thousands	4 Months Ended	12 Months Ended
	Apr. 30, 2018	Apr. 30, 2018	Apr. 30, 2017	Apr. 30, 2016
Current Provision [Abstract]
U.S. - Federal		$ (2,216)	$ 912	$ (5,365)
International		46,112	105,228	31,958
State and Local		961	100	1,657
Total Current Provision		44,857	106,240	28,250
Deferred Provision (Benefit) [Abstract]
U.S. - Federal		(26,062)	(13,852)	6,625
International		2,420	(15,330)	(6,459)
State and Local		530	415	595
Total Deferred (Benefit) Provision		(23,112)	(28,767)	761
Total Provision		21,745	77,473	29,011
Foreign and domestic pretax income [Abstract]
International		219,178	192,910	159,152
United States		(5,247)	(1,794)	15,641
Income Before Taxes		$ 213,931	$ 191,116	$ 174,793
Effective income tax rate reconciliation [Abstract]
U.S. Federal Statutory Rate	21.00%	30.40%	35.00%	35.00%
German Tax Litigation Expense		0.00%	25.70%	0.00%
Benefit from Lower Taxes on Non-U.S. Income		(8.40%)	(12.70%)	(14.60%)
State Income Taxes, Net of U.S. Federal Tax Benefit		0.40%	0.10%	0.80%
U.S. Tax Reform		(11.70%)	0.00%	0.00%
Deferred Tax Benefit From U.K. Statutory Tax Rate Change		0.00%	(1.30%)	(3.40%)
Tax Credits and Related Benefits		(1.70%)	(6.20%)	(1.60%)
Tax Adjustments and Other		1.20%	(0.10%)	0.40%
Effective Income Tax Rate		10.20%	40.50%	16.60%
Reduction in income tax expense resulting from estimated non-recurring items in the Tax Act		$ 25,100
Reduction in income tax expense resulting from estimated non-recurring items in the Tax Act (in dollars per share)		$ 0.43
Estimated net impact of non-recurring items from Tax Act excluding non-recurring items		21.90%
Income Tax Contingency [Line Items]
Recorded tax benefits due to expiration of statute of limitations and favorable resolutions of certain tax matters with tax authorities		$ (600)	$ 0	$ (1,300)
Income Tax Disclosure [Line Items]
Tax benefit related to re-measurement of net deferred tax liability		$ 47,000
Repatriation tax rate on foreign earnings held in cash equivalents and certain net assets		15.50%
Repatriation tax rate on foreign earnings held in other assets		8.00%
Provisional tax expense related to mandatory deemed repatriation tax on foreign earnings		$ 14,200
Valuation allowance on provisional tax expense related to mandatory deemed repatriation tax on foreign earnings	$ 6,500	6,500
Decrease in deferred tax assets due to utilization of foreign tax credit carryforwards		6,500
Accounting for uncertainty in income taxes [Abstract]
Accruals for interest and penalties	600	600	400
Net interest expense on reserves for unrecognized and recognized tax benefits		200	300
Total amount of unrecognized tax benefits that, if recognized, would reduce the Company's income tax provision	6,800	6,800	6,100
Reconciliation of unrecognized tax benefits [Roll Forward]
Balance, beginning of period		6,124	19,863
Additions for current year tax positions		1,372	2,566
Additions for prior year tax positions		69	31,802
Reductions for prior year tax positions		(38)	0
Foreign translation adjustment		45
Foreign translation adjustment			(419)
Payments and settlements		(124)	(47,688)
Reductions for lapse of statute of limitations		(615)	0
Balance, end of period	6,833	6,833	6,124	19,863
Income Tax Examination [Line Items]
Income tax charge related to unfavorable tax settlement		0	49,029	$ 0
Significant components of deferred tax assets and liabilities [Abstract]
Net Operating Losses	8,976	8,976	5,453
Reserve for Sales Returns and Doubtful Accounts	2,506	2,506	8,331
Accrued Employee Compensation	20,096	20,096	34,305
Foreign and Federal Credits	31,109	31,109	15,472
Other Accrued Expenses	4,632	4,632	14,303
Retirement and Post-Employment Benefits	39,160	39,160	56,633
Total Gross Deferred Tax Assets	106,479	106,479	134,497
Less Valuation Allowance	(8,811)	(8,811)	(1,300)
Total Deferred Tax Assets	97,668	97,668	133,197
Prepaid Expenses and Other Current Assets	(3,203)	(3,203)	(16,385)
Unremitted Foreign Earnings	(1,985)	(1,985)	0
Intangible and Fixed Assets	(231,869)	(231,869)	(272,008)
Total Deferred Tax Liabilities	(237,057)	(237,057)	(288,393)
Net Deferred Tax Liabilities	(139,389)	(139,389)	(155,196)
Reported As [Abstract]
Non-current Deferred Tax Assets	4,129	4,129	5,295
Non-current Deferred Tax Liabilities	(143,518)	(143,518)	(160,491)
Net Deferred Tax Liabilities	(139,389)	(139,389)	$ (155,196)
The Tax Act [Member]
Significant components of deferred tax assets and liabilities [Abstract]
Less Valuation Allowance	(6,500)	(6,500)
State and Federal Net Operating Loss Carryforwards [Member]
Significant components of deferred tax assets and liabilities [Abstract]
Less Valuation Allowance	(2,300)	$ (2,300)
U.K. [Member]
Income Tax Contingency [Line Items]
Foreign statutory tax rate		63.00%		19.00%
Foreign statutory tax rate in 2020			17.00%	18.00%
Tax benefit from the re-measurement legislation enacted			$ (2,600)	$ (5,900)
Deferred tax benefits associated with new tax legislation enacted (in dollars per share)			$ 0.04	$ 0.10
Germany [Member]
Income Tax Contingency [Line Items]
Foreign statutory tax rate		25.00%
Australia [Member]
Income Tax Contingency [Line Items]
Foreign statutory tax rate		7.00%
Foreign Tax Authority [Member]
Income Tax Disclosure [Line Items]
Accrued provisional tax liability	2,000	$ 2,000
Income Tax Examination [Line Items]
Income tax charge related to unfavorable tax settlement			$ 49,029
Income tax charge related to unfavorable tax settlement (in dollars per share)			$ 0.85
State and Local Jurisdiction [Member]
Income Tax Disclosure [Line Items]
Accrued provisional tax liability	100	100
Operating Loss Carryforwards [Line Items]
Net operating loss carry forwards	$ 81,000	81,000
Net operating loss carry forwards, tax effect		$ 4,800
State and Local Jurisdiction [Member] | Minimum [Member]
Operating Loss Carryforwards [Line Items]
Net operating loss carry forwards, expiration period		1 year
State and Local Jurisdiction [Member] | Maximum [Member]
Operating Loss Carryforwards [Line Items]
Net operating loss carry forwards, expiration period		20 years