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Income Taxes (Details) - USD ($)
$ / shares in Units, $ in Thousands
4 Months Ended 12 Months Ended
Apr. 30, 2018
Apr. 30, 2019
Apr. 30, 2018
Apr. 30, 2017
Apr. 30, 2016
Current Provision [Abstract]          
U.S. - Federal   $ 2,384 $ (2,216) $ 912  
International   52,518 46,112 105,228  
State and Local   2,536 961 100  
Total Current Provision   57,438 44,857 106,240  
Deferred Provision (Benefit) [Abstract]          
U.S. - Federal   335 (26,062) (13,852)  
International   (7,630) 2,420 (15,330)  
State and Local   (5,454) 530 415  
Total Deferred (Benefit) Provision   (12,749) (23,112) (28,767)  
Total Provision   44,689 21,745 77,473  
Foreign and domestic pretax income [Abstract]          
International   204,326 219,178 192,910  
United States   8,626 (5,247) (1,794)  
Income Before Taxes   $ 212,952 $ 213,931 $ 191,116  
Effective income tax rate reconciliation [Abstract]          
U.S. Federal Statutory Rate 21.00% 21.00% 30.40% 35.00%  
German Tax Litigation Expense   0.00% 0.00% 25.70%  
Cost (Benefit) of Higher (Lower) Taxes on Non-U.S. Income   0.90% (8.40%) (12.70%)  
State Income Taxes, net of U.S. Federal Tax Benefit   (1.30%) 0.40% 0.10%  
Deferred Tax (Benefit) from U.S. Tax Reform Rate Change   0.10% (11.70%) 0.00%  
Deferred Tax Benefit from U.K. Statutory Tax Rate Change   0.00% 0.00% (1.30%)  
Tax Credits and Related Benefits   (0.80%) (1.70%) (6.20%)  
Tax Adjustments and Other   1.10% 1.20% (0.10%)  
Effective Income Tax Rate   21.00% 10.20% 40.50%  
Expense recorded with completion of SAB 118 analysis (2019) and Provisional benefit amount recorded related to re-measurement of net deferred tax liability (2018)   $ 200 $ 25,000    
Estimated net impact of non-recurring items from Tax Act excluding non-recurring items   21.00% 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   $ 300 $ 600    
Income Tax Disclosure [Line Items]          
U.S. Federal Statutory Rate 21.00% 21.00% 30.40% 35.00%  
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      
Accounting for uncertainty in income taxes [Abstract]          
Accruals for interest and penalties $ 600 700 $ 600    
Net interest expense on reserves for unrecognized and recognized tax benefits   300 200    
Total amount of unrecognized tax benefits that, if recognized, would reduce the Company's income tax provision 6,800 7,700 6,800    
Reconciliation of unrecognized tax benefits [Roll Forward]          
Tax benefit related to Foreign Derived Intangible Income benefit   6,833 6,124    
Additions for Current Year Tax Positions   1,473 1,372    
Additions for Prior Year Tax Positions   414 69    
Reductions for Prior Year Tax Positions   (578) (38)    
Foreign Translation Adjustment   (42)      
Foreign Translation Adjustment     45    
Payments and Settlements   (136) (124)    
Reductions for Lapse of Statute of Limitations   (305) (615)    
Balance, end of period 6,833 7,659 6,833 $ 6,124  
Income Tax Examination [Line Items]          
Income tax charge related to unfavorable tax settlement   0 0 $ 49,029  
Significant components of deferred tax assets and liabilities [Abstract]          
Net Operating Losses 8,976 14,491 8,976    
Reserve for Sales Returns and Doubtful Accounts 2,506 2,923 2,506    
Accrued Employee Compensation 20,096 17,528 20,096    
Foreign and Federal Credits 31,109 34,401 31,109    
Other Accrued Expenses 4,632 6,262 4,632    
Retirement and Post-Employment Benefits 39,160 40,653 39,160    
Total Gross Deferred Tax Assets 106,479 116,258 106,479    
Less Valuation Allowance (8,811) (21,179) (8,811)    
Total Deferred Tax Assets 97,668 95,079 97,668    
Prepaid Expenses and Other Current Assets (3,203) (744) (3,203)    
Unremitted Foreign Earnings (1,985) (1,985) (1,985)    
Intangible and Fixed Assets (231,869) (226,898) (231,869)    
Total Deferred Tax Liabilities (237,057) (229,627) (237,057)    
Net Deferred Tax Liabilities (139,389) (134,548) (139,389)    
Reported As [Abstract]          
Non-current Deferred Tax Assets 4,129 9,227 4,129    
Non-current Deferred Tax Liabilities (143,518) (143,775) (143,518)    
Net Deferred Tax Liabilities $ (139,389) $ (134,548) $ (139,389)    
U.K. [Member]          
Income Tax Contingency [Line Items]          
Foreign statutory tax rate   57.00%     19.00%
Foreign statutory tax rate in 2020       17.00% 18.00%
Tax benefit from the re-measurement legislation enacted       $ (2,600)  
Deferred tax benefits associated with new tax legislation enacted (in dollars per share)       $ 0.04  
Germany [Member]          
Income Tax Contingency [Line Items]          
Foreign statutory tax rate   24.00%      
Australia [Member]          
Income Tax Contingency [Line Items]          
Foreign statutory tax rate   7.00%      
Foreign Tax Authority [Member]          
Effective income tax rate reconciliation [Abstract]          
U.S. Federal Statutory Rate   13.125%      
Income Tax Disclosure [Line Items]          
U.S. Federal Statutory Rate   13.125%      
Estimated taxes upon repatriation   $ 2,000      
Reconciliation of unrecognized tax benefits [Roll Forward]          
Balance, end of period   1,200      
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]          
Operating Loss Carryforwards [Line Items]          
Net operating loss carry forwards   99,000      
Net operating loss carry forwards, tax effect   $ 6,000      
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