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Employee Benefit Plans - Schedule of Funded Status and Amounts Recognized in the Balance Sheet (Details) - USD ($)
$ in Millions
 12 Months Ended
Jun. 01, 2024
Jun. 03, 2023
May 28, 2022
Components of the amounts recognized in the Consolidated Balance Sheets:      
Non-current liabilities $ 10.0 $ 7.5  
Domestic | Pension Plan      
Change in benefit obligation:      
Benefit obligation at beginning of year 123.8 152.6  
Interest cost 6.1 6.1 $ 3.9
Expected Administrative Expenses 0.0 0.6  
Loss related to settlement 0.0 4.7  
Foreign exchange impact 0.0 0.0  
Actuarial loss (gain) 4.4 (18.2)  
Administrative expenses paid 0.0 (0.7)  
Benefits paid (8.4) (7.2)  
Benefits paid related to settlement 0.0 (14.1)  
Benefit obligation at end of year 125.9 123.8 152.6
Change in plan assets:      
Fair value of plan assets at beginning of year 126.3 144.0  
Actual return on plan assets 5.7 (2.9)  
Foreign exchange impact 0.0 0.0  
Employer contributions 0.1 7.2  
Actual expenses paid (0.6) (0.7)  
Benefits paid (8.4) (21.3)  
Fair value of plan assets at end of year 123.1 126.3 144.0
Funded status:      
Over (under) funded status at end of year (2.8) 2.5  
Components of the amounts recognized in the Consolidated Balance Sheets:      
Current assets 0.0 0.0  
Non-current assets 0.0 2.5  
Current liabilities 0.0 0.0  
Non-current liabilities 2.8 0.0  
Components of the amounts recognized in Accumulated other comprehensive loss before the effect of income taxes:      
Prior service cost 0.0 0.0  
Unrecognized net actuarial loss (gain) 3.5 (4.4)  
Accumulated other comprehensive loss (gain) 3.5 (4.4)  
International      
Change in benefit obligation:      
Expected Administrative Expenses   0.0  
Loss related to settlement   0.0  
Administrative expenses paid   0.0  
Benefits paid related to settlement   0.0  
International | Pension Plan      
Change in benefit obligation:      
Benefit obligation at beginning of year 76.0 104.5  
Interest cost 4.1 3.1 2.4
Expected Administrative Expenses 0.0    
Loss related to settlement 0.0    
Foreign exchange impact 1.8 (2.5)  
Actuarial loss (gain) 2.6 (26.2)  
Administrative expenses paid 0.0    
Benefits paid (3.3) (2.9)  
Benefits paid related to settlement 0.0    
Benefit obligation at end of year 81.2 76.0 104.5
Change in plan assets:      
Fair value of plan assets at beginning of year 84.4 93.5  
Actual return on plan assets 4.5 (9.1)  
Foreign exchange impact 2.0 (1.6)  
Employer contributions 1.7 4.5  
Actual expenses paid 0.0 0.0  
Benefits paid (3.3) (2.9)  
Fair value of plan assets at end of year 89.3 84.4 $ 93.5
Funded status:      
Over (under) funded status at end of year 8.1 8.4  
Components of the amounts recognized in the Consolidated Balance Sheets:      
Current assets 0.0 0.0  
Non-current assets 8.1 8.4  
Current liabilities 0.0 0.0  
Non-current liabilities 0.0 0.0  
Components of the amounts recognized in Accumulated other comprehensive loss before the effect of income taxes:      
Prior service cost 0.4 0.4  
Unrecognized net actuarial loss (gain) 29.2 25.7  
Accumulated other comprehensive loss (gain) $ 29.6 $ 26.1