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Debt (Schedule of Long-term Debt) (Details)
3 Months Ended
Apr. 03, 2021
USD ($)
Apr. 03, 2021
EUR (€)
Jan. 02, 2021
USD ($)
Apr. 03, 2019
USD ($)
May 02, 2018
EUR (€)
Debt Instrument [Line Items]          
Debt and Lease Obligation $ 1,444,531,000   $ 1,508,069,000    
Current portion of long-term debt 26,997,000   27,538,000    
Long-term debt, net of current portion $ 1,417,534,000   1,480,531,000    
Capital Lease Obligations | €   € 2,800,000      
Senior Secured Facilities [Member]          
Debt Instrument [Line Items]          
Line of credit term 5 years        
Term Loan B Facility [Member] | Senior Secured Facilities [Member]          
Debt Instrument [Line Items]          
Long-term Debt $ 247,021,000   296,202,000    
Long-term Debt, Gross 250,000,000   300,000,000    
Unamortized Debt Issuance Expense (2,979,000)   (3,798,000)    
Senior Notes [Member] | Senior Notes 5.25% Due 2027 [Member]          
Debt Instrument [Line Items]          
Long-term Debt 494,447,000   494,253,000    
Long-term Debt, Gross 500,000,000   500,000,000    
Unamortized Debt Issuance Expense $ (5,553,000)   (5,747,000)    
Stated interest rate 5.25% 5.25%   5.25%  
Debt instrument, interest rate, effective percentage 5.47% 5.47%      
Face amount of debt instrument       $ 500,000,000.0  
Senior Notes [Member] | Senior Notes 3.625% Due 2026 [Member]          
Debt Instrument [Line Items]          
Long-term Debt $ 600,264,000   625,577,000    
Long-term Debt, Gross 606,310,000   632,163,000    
Unamortized Debt Issuance Expense $ (6,046,000)   (6,586,000)    
Line of credit outstanding | €   € 515,000,000.0      
Stated interest rate 3.625% 3.625%     3.625%
Debt instrument, interest rate, effective percentage 3.83% 3.83%      
Face amount of debt instrument | €         € 515,000,000.0
Notes Payable, Other Payables [Member]          
Debt Instrument [Line Items]          
Long-term Debt $ 33,799,000   37,037,000    
Notes Payable, Other Payables [Member] | Other Debt Obligations [Member]          
Debt Instrument [Line Items]          
Long-term Debt 12,900,000        
Notes Payable, Other Payables [Member] | Bank Overdrafts [Member]          
Debt Instrument [Line Items]          
Long-term Debt 4,700,000        
Foreign Line of Credit [Member] | Senior Secured Facilities [Member]          
Debt Instrument [Line Items]          
Line of credit outstanding 11,700,000        
Foreign Line of Credit [Member] | Notes Payable, Other Payables [Member]          
Debt Instrument [Line Items]          
Line of credit outstanding 16,200,000        
Letter of Credit [Member] | Senior Secured Facilities [Member]          
Debt Instrument [Line Items]          
Line of credit outstanding 3,800,000        
Revolving Credit Facility [Member] | Line of Credit [Member] | Senior Secured Facilities [Member]          
Debt Instrument [Line Items]          
Long-term Debt 69,000,000   $ 55,000,000    
Term Loan B Facility [Member] | Senior Secured Facilities [Member]          
Debt Instrument [Line Items]          
Face amount of debt instrument 525,000,000.0        
U.S. dollar | Term Loan B Facility [Member] | Senior Secured Facilities [Member]          
Debt Instrument [Line Items]          
Line of credit outstanding $ 250,000,000.0        
London Interbank Offered Rate (LIBOR) [Member] | Secured Debt [Member] | Senior Secured Facilities [Member]          
Debt Instrument [Line Items]          
Basis spread on variable rate 1.50%        
Interest rate 1.616% 1.616%      
London Interbank Offered Rate (LIBOR) [Member] | U.S. dollar | Revolving Credit Facility [Member] | Senior Secured Facilities [Member]          
Debt Instrument [Line Items]          
Line of credit outstanding $ 42,000,000.0        
London Interbank Offered Rate (LIBOR) [Member] | U.S. dollar | Term Loan B Facility [Member] | Senior Secured Facilities [Member]          
Debt Instrument [Line Items]          
Basis spread on variable rate 2.00%        
Interest rate 2.12% 2.12%      
Base Rate [Member] | U.S. dollar | Secured Debt [Member] | Senior Secured Facilities [Member]          
Debt Instrument [Line Items]          
Basis spread on variable rate 0.50%        
Interest rate 3.75% 3.75%      
Base Rate [Member] | U.S. dollar | Revolving Credit Facility [Member] | Senior Secured Facilities [Member]          
Debt Instrument [Line Items]          
Line of credit outstanding $ 27,000,000.0