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Revenue Recognition - Reserves for Variable Consideration and Credit Risk (Details) - USD ($)
$ in Thousands
 12 Months Ended
Jan. 02, 2021
Dec. 28, 2019
Dec. 29, 2018
Dec. 30, 2017
Disaggregation of Revenue        
Allowance for doubtful accounts $ 700 $ 400    
Roll forward of the variable consideration and allowances for accounts receivable        
Balance at, beginning of year 3,838 3,764    
Increases to reserves, net of recoveries 2,092 2,926    
Amounts written off and foreign currency translation (2,335) (2,852)    
Balance at, end of year 3,595 3,838 $ 3,764  
Cumulative effect of a change in accounting principle related to ASC 326 209,019 197,751 196,472 $ 207,229
Roll forward of the variable consideration and allowances for unbilled services        
Balance at beginning of year 1,503 415    
Increases to reserves, net of recoveries 6,847 5,548    
Amounts written off and foreign currency translation (7,350) (4,460)    
Balance at end of year 1,000 1,503 415  
Accounts receivable allowances (479) 47 (1,410)  
Reimbursable expenses 61,661 54,871 48,817  
Retained Earnings        
Roll forward of the variable consideration and allowances for accounts receivable        
Cumulative effect of a change in accounting principle related to ASC 326 216,999 200,249 186,229 $ 169,390
Cumulative Effect Period of Adoption, Adjustment | ASC 326        
Roll forward of the variable consideration and allowances for accounts receivable        
Cumulative effect of a change in accounting principle related to ASC 326   (203)    
Cumulative Effect Period of Adoption, Adjustment | Retained Earnings | ASC 326        
Roll forward of the variable consideration and allowances for accounts receivable        
Cumulative effect of a change in accounting principle related to ASC 326   (203)    
Selling, general and administrative expenses        
Roll forward of the variable consideration and allowances for unbilled services        
Accounts receivable allowances $ 227 $ 173 $ 1,237