v3.25.4
Share-based Compensation - Narrative (Details) - USD ($)
12 Months Ended
Dec. 28, 2025
Dec. 29, 2024
Dec. 31, 2023
Jan. 01, 2023
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Noncash expense $ 12,865,000 $ 35,149,000 $ 24,196,000  
KKI        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Vested (in shares)   0   0
Restricted Stock Units (RSUs) | KKI        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Total vested fair value 26,900,000 $ 28,100,000 7,800,000  
Restricted Stock Units (RSUs) | KK U.K.        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Total vested fair value $ 100,000 $ 0 700,000  
Vested (in shares) 5,000 0    
Restricted Stock Units (RSUs) | KK Australia        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Total vested fair value $ 200,000 $ 100,000 200,000  
Vested (in shares) 116,000 42,000    
Restricted Stock Units (RSUs) | KK Mexico        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Total vested fair value $ 500,000 $ 100,000 0  
Vested (in shares) 17,000 2,000    
Restricted Stock Units (RSUs), Fifty-Four Month Vesting        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Award vesting period 54 months      
Restricted Stock Units (RSUs), Sixty Month Vesting Period        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Award vesting period 60 months      
Restricted Stock Units (RSUs), Sixty Month Vesting Period | Share-based Payment Arrangement, Tranche One        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Vesting percentage 60.00%      
Restricted Stock Units (RSUs), Sixty Month Vesting Period | Share-based Payment Arrangement, Tranche Two        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Vesting percentage 20.00%      
Restricted Stock Units (RSUs), Sixty Month Vesting Period | Share-based Payment Arrangement, Tranche Three        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Vesting percentage 20.00%      
Stock Options        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Noncash expense $ (100,000) $ 5,300,000 3,600,000  
Service period 6 years      
Performance Stock Units (PSUs) | Maximum        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Target amounts 200.00%      
Performance Stock Units (PSUs) | Minimum        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Target amounts 0.00%      
Restricted Stock Units (RSUs) and Performance Stock Units (PSUs)        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Noncash expense $ 12,700,000 30,000,000.0 20,600,000  
Tax (expense)/benefit $ (2,100,000) $ (1,200,000) $ (2,100,000)  
Restricted Stock Units (RSUs) and Performance Stock Units (PSUs) | KKI        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Vested (in shares) 1,805,000 1,893,000    
Restricted Stock Units (RSUs), Thirty-Six Month Vesting        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Award vesting period 36 months      
Restricted Stock Units (RSUs), Twenty-Four Month Vesting        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Award vesting period 24 months      
Restricted Stock Units (RSUs), Twenty-Four Month Vesting | Share-based Payment Arrangement, Tranche One        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Vesting percentage 60.00%      
Restricted Stock Units (RSUs), Twenty-Four Month Vesting | Share-based Payment Arrangement, Tranche Two        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Vesting percentage 40.00%      
Share-Based Payment Arrangement, Option, Sixty Months        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Award vesting period 60 months      
Service period 10 years      
Share-Based Payment Arrangement, Option, Sixty Months | Share-based Payment Arrangement, Tranche One        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Vesting percentage 60.00%      
Share-Based Payment Arrangement, Option, Sixty Months | Share-based Payment Arrangement, Tranche Two        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Vesting percentage 20.00%      
Share-Based Payment Arrangement, Option, Sixty Months | Share-based Payment Arrangement, Tranche Three        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Vesting percentage 20.00%      
Share-Based Payment Arrangement, Option, Thirty-Six Months        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Award vesting period 36 months