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Income Tax Expense (Details) - USD ($)
$ / shares in Units, $ in Thousands
 12 Months Ended
Mar. 31, 2023
Mar. 31, 2022
Mar. 31, 2021
May 21, 2021
Operating Loss Carryforwards [Line Items]        
Income Tax Examination, Penalties and Interest Accrued $ 152 $ 152    
Unrecognized Tax Benefits that Would Impact Effective Tax Rate 2,640      
Uncertain Tax Liability Resulting From IRS Notice 12,000     $ 50,000
Deferred Tax Assets, Tax Credit Carryforwards 35,220      
Deferred Tax Assets, Tax Deferred Expense, Compensation and Benefits, Postretirement Benefits $ 1,737 $ 2,086    
Effective Income Tax Rate Reconciliation, at Federal Statutory Income Tax Rate 12.50% 12.50% 12.50%  
Current Federal Tax Expense (Benefit) $ 8,837 $ 12,002 $ 9,244  
Effective Income Tax Rate, Continuing Operations 32.80% 22.80% 23.30%  
Unrecognized Tax Benefits $ 2,487 $ 2,906 $ 2,295  
Current State and Local Tax Expense (Benefit) 33,234 21,438 16,272  
Current Income Tax Expense (Benefit) 241,725 174,952 119,765  
Deferred Federal Income Tax Expense (Benefit) (864) (739) (787)  
Deferred State and Local Income Tax Expense (Benefit) (50,530) (17,124) (550)  
Increase (Decrease) in Deferred Income Taxes (190,190) (103,319) 898  
Income Tax Expense (Benefit) $ 51,535 $ 71,633 $ 120,663  
Effective Income Tax Rate Reconciliation, State and Local Income Taxes (10.80%) 1.40% 2.40%  
Effective Income Tax Rate Reconciliation, Change in Deferred Tax Assets Valuation Allowance, Percent (0.10%) 0.90% 0.30%  
Effective Tax Rate Reconciliation, Increase (decrease) in Valuation Allowances (0.10%) 0.20% (0.10%)  
Effective Income Tax Rate Reconciliation, Tax Credit, Research, Percent (1.80%) (0.80%) (0.50%)  
Effective Income Tax Rate Reconciliation, Tax Credits, Foreign (1.20%) (1.10%) (0.30%)  
Effective Income Tax Rate Reconciliation, Foreign Income Tax Rate Differential 8.60% 12.60% 8.30%  
Effective Tax Rate Reconciliation, UK Tax Rate Differential 0.00% 0.00% 2.10%  
Effective Income Tax Rate Reconciliation, Tax Expense (Benefit), Share-based Payment Arrangement, Percent (2.70%) (5.10%) (1.90%)  
Effective Tax Reconciliation, deferred tax assets and liabilities 0.40% 2.30% 0.40%  
U.S. tax reform impact GILTI and FDII (1.30%) (0.90%) (0.60%)  
Effective Income Tax Rate Reconciliation, Nondeductible Expense, Impairment Losses, Percent 29.00% 0.00% 0.00%  
Capitalized Interest Costs- Effective tax rate 0.00% 1.80% 0.60%  
Effective Income Tax Rate Reconciliation, Other Adjustments 0.30% (1.00%) 0.10%  
Unrecognized Tax Benefits, Increases Resulting from Current Period Tax Positions $ 63 $ 0    
Unrecognized Tax Benefits, Decrease Resulting from Current Period Tax Positions 0 (135)    
Unrecognized Tax Benefits, Increase Resulting from Acquisition   (746)    
Unrecognized Tax Benefits, Increase Resulting from Foreign Currency Translation 21 0    
Unrecognized Tax Benefits, Decrease Resulting from Acquisition (503)      
Deferred Tax Assets, Tax Deferred Expense, Compensation and Benefits 15,858 14,340    
Deferred Tax Assets, Operating Loss Carryforwards 9,407      
Deferred Tax Assets, Tax Deferred Expense, Reserves and Accruals, Accrued Liabilities 13,150 12,092    
Deferred Tax Assets, Tax Deferred Expense, Reserves and Accruals, Self Insurance 2,268 2,561    
Deferred Tax Assets, Deferred Income 23,967 20,688    
Deferred Tax Assets, Tax Deferred Expense, Reserves and Accruals, Allowance for Doubtful Accounts 3,763 2,187    
Deferred Tax Assets, in Process Research and Development 15,382 0    
Deferred Tax Assets, Operating leases 46,781 44,401    
Deferred Tax Assets, Tax Credit Carryforwards, Foreign 33,559 36,036    
Deferred Tax Liabilities, Leasing Arrangements 45,834 43,593    
Deferred Tax Assets, Other 11,701 8,579    
Deferred Tax Assets, Gross, Current 205,833 168,520    
Deferred Tax Assets, Valuation Allowance 20,315 24,691    
Deferred Tax Assets, Net of Valuation Allowance 185,518 143,829    
Deferred Tax Liabilities, Property, Plant and Equipment 98,601 110,951    
Deferred Tax Liabilities, Goodwill and Intangible Assets, Intangible Assets 630,589 755,980    
Deferred Tax Liabilities, Pension 2,644 2,004    
Deferred Tax and Other Liabilities, Noncurrent 3,186 3,473    
Deferred tax liabilities, net of deferred tax assets 780,854 916,001    
Deferred Tax Liabilities (595,336) (772,172)    
Deferred Tax Assets, Operating Loss Carryforwards, Foreign 126,443      
Deferred Tax Assets, Operating Loss Carryforwards, State and Local 3,391      
Valuation Allowance, Deferred Tax Asset, Change in Amount (4,376)      
Deferred Tax Assets, Operating Loss Carryforwards 37,667 25,550    
Undistributed Earnings of Foreign Subsidiaries 1,915,000      
IRS settlement paid 7,500      
Deferred tax Asset Credit Carryforward, German Branches 26,728      
Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest 157,348 314,503 $ 517,533  
Costa Rica Exempt thorugh 2025 and partially exempt through 2029 [Member]        
Operating Loss Carryforwards [Line Items]        
Income Tax Holiday, Aggregate Dollar Amount $ 2,000      
Income Tax Holiday, Income Tax Benefits Per Share $ 0.02      
UNITED STATES        
Operating Loss Carryforwards [Line Items]        
Income (Loss) from Continuing Operations before Income Taxes, Foreign $ (16,759) 79,662 326,991  
Current Foreign Tax Expense (Benefit) 138,208 88,158 57,550  
Deferred Foreign Income Tax Expense (Benefit) (114,523) (73,833) 7,523  
Other Foreign Entities [Member]        
Operating Loss Carryforwards [Line Items]        
Income (Loss) from Continuing Operations before Income Taxes, Foreign 111,443 146,763 117,100  
Current Foreign Tax Expense (Benefit) 61,446 53,354 36,699  
Deferred Foreign Income Tax Expense (Benefit) (24,273) (11,623) (5,288)  
IRELAND        
Operating Loss Carryforwards [Line Items]        
Income (Loss) from Continuing Operations before Income Taxes, Domestic $ 62,664 $ 88,078 $ 73,442