Income Tax Expense (Details)
$ / shares in Units, $ in Thousands
 12 Months Ended
Mar. 31, 2020
USD ($)
$ / shares
Mar. 31, 2019
USD ($)
Mar. 31, 2018
USD ($)
Mar. 31, 2017
USD ($)
Operating Loss Carryforwards [Line Items]        
TCJA Effective U.S. Federal Tax Rate 0.210      
Income Tax Examination, Penalties and Interest Accrued $ 243 $ 360    
Unrecognized Tax Benefits that Would Impact Effective Tax Rate 1,118      
Uncertain Tax Liability Resulting From IRS Notice 40,000      
Deferred Tax Assets, Tax Credit Carryforwards 2,547      
Deferred Tax Assets, Tax Deferred Expense, Compensation and Benefits, Postretirement Benefits $ 2,871 $ 3,142    
Effective Income Tax Rate Reconciliation, at Federal Statutory Income Tax Rate 12.50% 12.50% 19.00%  
Current Federal Tax Expense (Benefit) $ 5,036 $ 2,627 $ 2,596  
Income (Loss) from Continuing Operations before Income Taxes, Domestic $ 29,543 $ 13,693 $ 11,837  
Effective Income Tax Rate, Continuing Operations 18.20% 17.40% 17.80%  
Unrecognized Tax Benefits $ 875 $ 2,314 $ 2,500  
Income (Loss) from Continuing Operations before Equity Method Investments, Income Taxes, Noncontrolling Interest 498,681 369,470 354,982  
Current State and Local Tax Expense (Benefit) 9,971 12,484 7,727  
Current Income Tax Expense (Benefit) 81,639 71,878 84,793  
Deferred Federal Income Tax Expense (Benefit) (899) (546) (280)  
Deferred State and Local Income Tax Expense (Benefit) 2,363 2,836 2,656  
Increase (Decrease) in Deferred Income Taxes 9,237 (7,484) (21,433)  
Income Tax Expense (Benefit) $ 90,876 $ 64,394 $ 63,360  
Effective Income Tax Rate Reconciliation, State and Local Income Taxes 2.00% 3.10% 2.30%  
Effective Income Tax Rate Reconciliation, Change in Deferred Tax Assets Valuation Allowance, Percent 0.50% 0.40% 0.10%  
Effective Tax Rate Reconciliation, Increase (decrease) in Valuation Allowances (0.30%) 0.00% 0.10%  
Effective Income Tax Rate Reconciliation, Tax Credit, Research, Percent (0.50%) (0.60%) (0.50%)  
Effective Income Tax Rate Reconciliation, Tax Credits, Foreign (0.60%) (0.20%) (0.20%)  
Effective Income Tax Rate Reconciliation, Foreign Income Tax Rate Differential 6.90% 4.50% 0.00%  
Effective Tax Rate Reconciliation, UK Tax Rate Differential 0.00% 0.00% 4.10%  
Effective Income Tax Rate Reconciliation, Deductions, Qualified Production Activities 0.00% 0.00% (0.80%)  
Effective Income Tax Rate Reconciliation, Tax Expense (Benefit), Share-based Payment Arrangement, Percent (2.80%) (2.20%) (1.80%)  
Effective Tax Reconciliation, deferred tax assets and liabilities 0.10% (0.60%) (10.30%)  
Change in Effective Income Tax US Transition tax 0.00% (0.30%) 4.90%  
U.S. tax reform impact GILTI and FDII 0.10% 0.30% 0.00%  
Effective Tax Rate Reconciliation, acquisitions and divestitures 0.00% 0.00% 0.50%  
Capitalized Interest Costs- Effective tax rate 0.10% 0.50% 0.00%  
Effective Income Tax Rate Reconciliation, Other Adjustments 0.20% 0.00% 0.40%  
Unrecognized Tax Benefits, Increases Resulting from Current Period Tax Positions $ 176 $ 178    
Unrecognized Tax Benefits, Decrease Resulting from Current Period Tax Positions (1,570) (186)    
Unrecognized Tax Benefits, Decrease Resulting from Foreign Currency Translation (45) (178)    
Deferred Tax Assets, Tax Deferred Expense, Compensation and Benefits 12,560 14,275    
Deferred Tax Assets, Operating Loss Carryforwards 10,942      
Deferred Tax Assets, Tax Deferred Expense, Reserves and Accruals, Accrued Liabilities 5,490 4,858    
Deferred Tax Assets, Tax Deferred Expense, Reserves and Accruals, Self Insurance 3,620 3,187    
Deferred Tax Assets, Deferred Income 11,316 7,509    
Deferred Tax Assets, Tax Deferred Expense, Reserves and Accruals, Allowance for Doubtful Accounts 1,820 1,386    
Deferred Tax Assets, Tax Deferred Expense, Compensation and Benefits, Pensions 2,273 3,364    
Deferred Tax Assets, Operating leases 28,945 0    
Deferred Tax Liabilities, Leasing Arrangements 29,268 0    
Deferred Tax Assets, Other 6,024 7,707    
Deferred Tax Assets, Gross, Current 91,068 64,623    
Deferred Tax Assets, Valuation Allowance 13,891 13,478 $ 13,596 $ 16,366
Deferred Tax Assets, Net of Valuation Allowance 77,177 51,145    
Deferred Tax Liabilities, Property, Plant and Equipment 68,179 61,060    
Deferred Tax Liabilities, Goodwill and Intangible Assets, Intangible Assets 129,951 128,479    
Deferred Tax and Other Liabilities, Noncurrent 2,078 2,197    
Deferred tax liabilities, net of deferred tax assets 229,476 191,736    
Deferred Tax Liabilities (152,299) (140,591)    
Deferred Tax Assets, Operating Loss Carryforwards, Foreign 41,450      
Deferred Tax Assets, Operating Loss Carryforwards, State and Local 2,042      
Valuation Allowance, Deferred Tax Asset, Change in Amount 413      
Deferred Tax Assets, Operating Loss Carryforwards 16,149 19,195    
Undistributed Earnings of Foreign Subsidiaries 1,600,000      
Costa Rica Exempt thorugh 2025 and partially exempt through 2029 [Member]        
Operating Loss Carryforwards [Line Items]        
Income Tax Holiday, Aggregate Dollar Amount $ 1,900      
Income Tax Holiday, Income Tax Benefits Per Share | $ / shares $ 0.02      
UNITED STATES        
Operating Loss Carryforwards [Line Items]        
Income (Loss) from Continuing Operations before Income Taxes, Foreign $ 325,522 235,405 203,872  
Current Foreign Tax Expense (Benefit) 42,032 29,943 47,728  
Deferred Foreign Income Tax Expense (Benefit) 10,073 5,775 (15,728)  
Other Foreign Entities [Member]        
Operating Loss Carryforwards [Line Items]        
Income (Loss) from Continuing Operations before Income Taxes, Foreign 143,616 120,372 139,273  
Current Foreign Tax Expense (Benefit) 24,600 26,824 26,742  
Deferred Foreign Income Tax Expense (Benefit) (2,300) $ (15,549) $ (8,081)  
Maximum [Member]        
Operating Loss Carryforwards [Line Items]        
Tax Cuts and Jobs Act, Incomplete Accounting, Provisional Income Tax Expense (Benefit) $ 15,000