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Debt (Schedule of Long-term Debt) (Details)
$ in Thousands, € in Millions
9 Months Ended
Oct. 02, 2021
USD ($)
Oct. 02, 2021
EUR (€)
Jan. 02, 2021
USD ($)
Debt Instrument [Line Items]      
Debt and Lease Obligation $ 1,380,874   $ 1,508,069
Current portion of long-term debt 55,138   27,538
Long-term debt, net of current portion 1,325,736   1,480,531
Finance lease obligations | €   € 2.5  
Term Loan B Facility [Member] | Senior Secured Facilities [Member]      
Debt Instrument [Line Items]      
Long-term Debt 197,919   296,202
Long-term Debt, Gross 200,000   300,000
Unamortized Debt Issuance Expense (2,081)   (3,798)
Senior Notes [Member] | Senior Notes 5.25% Due 2027 [Member]      
Debt Instrument [Line Items]      
Long-term Debt 494,841   494,253
Long-term Debt, Gross 500,000   500,000
Unamortized Debt Issuance Expense $ (5,159)   (5,747)
Stated interest rate 5.25% 5.25%  
Debt instrument, interest rate, effective percentage 5.47% 5.47%  
Senior Notes [Member] | Senior Notes 3.625% Due 2026 [Member]      
Debt Instrument [Line Items]      
Long-term Debt $ 591,874   625,577
Long-term Debt, Gross 597,297   632,163
Unamortized Debt Issuance Expense $ (5,423)   (6,586)
Line of credit outstanding | €   € 515.0  
Stated interest rate 3.625% 3.625%  
Debt instrument, interest rate, effective percentage 3.83% 3.83%  
Notes Payable, Other Payables [Member]      
Debt Instrument [Line Items]      
Long-term Debt $ 63,240   37,037
Notes Payable, Other Payables [Member] | Other Debt Obligations [Member]      
Debt Instrument [Line Items]      
Long-term Debt 11,100    
Notes Payable, Other Payables [Member] | Bank Overdrafts [Member]      
Debt Instrument [Line Items]      
Long-term Debt 32,900    
Foreign Line of Credit [Member] | Senior Secured Facilities [Member]      
Debt Instrument [Line Items]      
Line of credit outstanding 11,800    
Foreign Line of Credit [Member] | Notes Payable, Other Payables [Member]      
Debt Instrument [Line Items]      
Line of credit outstanding 19,200    
Letter of Credit [Member] | Senior Secured Facilities [Member]      
Debt Instrument [Line Items]      
Line of credit outstanding 4,100    
Revolving Credit Facility [Member] | Line of Credit [Member] | Senior Secured Facilities [Member]      
Debt Instrument [Line Items]      
Long-term Debt 33,000   $ 55,000
U.S. dollar | Term Loan B Facility [Member] | Senior Secured Facilities [Member]      
Debt Instrument [Line Items]      
Line of credit outstanding $ 200,000    
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 2.09% 2.09%  
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 $ 33,000