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Stockholders' Equity and Noncontrolling Interests - (Components of Accumulated Other Comprehensive Income) (Details) - USD ($)
$ in Thousands
 3 Months Ended 6 Months Ended
Sep. 29, 2024
Jun. 30, 2024
Oct. 01, 2023
Jul. 02, 2023
Sep. 29, 2024
Sep. 29, 2022
Accumulated Other Comprehensive Income (Loss), Net of Tax [Abstract]            
Beginning balance $ 1,811,189 $ 1,757,072 $ 1,683,179 $ 1,603,881 $ 1,757,072  
Ending balance 1,841,596 1,811,189 1,663,381 1,683,179 1,841,596  
Cross Currency Fixed Interest Rate Contract | Designated as Hedging Instrument            
Accumulated Other Comprehensive Income (Loss), Net of Tax [Abstract]            
Derivative notional amount 300       300 $ 150,000
Pension funded status adjustment            
Accumulated Other Comprehensive Income (Loss), Net of Tax [Abstract]            
Beginning balance   (9,798)     (9,798)  
Before Reclassifications         0  
Ending balance (9,601)       (9,601)  
Foreign currency translation adjustment, gain         0  
Net unrealized gain (loss) on derivative instruments            
Accumulated Other Comprehensive Income (Loss), Net of Tax [Abstract]            
Beginning balance   755     755  
Before Reclassifications         (2,923)  
Amounts Reclassified from AOCI         (1,257)  
Ending balance (3,425)       (3,425)  
Foreign currency translation adjustment, gain         (2,923)  
Foreign currency translation adjustment            
Accumulated Other Comprehensive Income (Loss), Net of Tax [Abstract]            
Beginning balance   (195,808)     (195,808)  
Before Reclassifications 28,685 (13,294) (31,647) 2,192 15,391  
Amounts Reclassified from AOCI         0  
Ending balance (180,417)       (180,417)  
Foreign currency translation adjustment, gain 28,685 (13,294) $ (31,647) $ 2,192 15,391  
Foreign currency translation adjustment | Cross currency fixed interest rate swaps | Net investment hedges | Designated as Hedging Instrument            
Accumulated Other Comprehensive Income (Loss), Net of Tax [Abstract]            
Before Reclassifications         8,497  
Foreign currency translation adjustment, gain         8,497  
Foreign currency translation adjustment, tax         2,594  
Accumulated other comprehensive (loss) income            
Accumulated Other Comprehensive Income (Loss), Net of Tax [Abstract]            
Beginning balance   $ (204,851)     (204,851)  
Before Reclassifications         12,468  
Amounts Reclassified from AOCI         (1,060)  
Ending balance $ (193,443)       (193,443)  
Foreign currency translation adjustment, gain         $ 12,468