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Employee Benefit Plans - Funded Status (Details) (USD $)
In Millions, unless otherwise specified
 12 Months Ended
Jun. 01, 2013
Jun. 02, 2012
May 28, 2011
The components of the amounts recognized in the Consolidated Balance Sheets are as follows.      
Current liabilities $ (1.1) $ (1.2)  
Non-current liabilities (39.6) (37.9)  
Pension Benefits, Domestic [Member]
      
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]      
Defined Benefit Plan, Settlements, Plan Assets (40.0) 0  
Change in benefit obligation:      
Benefit obligation at beginning of year 332.7 309.9  
Service cost 1.9 7.0 6.9
Interest cost 10.9 14.4 15.1
Defined Benefit Plan, Curtailments 0 4.3  
Defined Benefit Plan, Recognized Net Gain (Loss) Due to Settlements (40.0) 0  
Foreign exchange impact 0 0  
Actuarial (gain)/loss 15.6 22.4  
Employee contributions 0 0  
Benefits paid (6.4) (16.7)  
Benefit obligation at end of year 314.7 332.7 309.9
Change in plan assets:      
Fair value of plan assets at beginning of year 316.9 273.4  
Actual return on plan assets 19.5 10.0  
Foreign exchange impact 0 0  
Employer contributions 0 50.2  
Employee contributions 0 0  
Benefits paid (6.4) (16.7)  
Fair value of plan assets at end of year 290.0 316.9 273.4
Funded status:      
Under funded status at end of year (24.7) (15.8)  
The components of the amounts recognized in the Consolidated Balance Sheets are as follows.      
Current liabilities (0.1) (0.1)  
Non-current liabilities (24.6) (15.7)  
The components of the amounts recognized in accumulated other comprehensive loss before the effect of income taxes are as follows.      
Unrecognized net actuarial loss 140.5 162.8  
Unrecognized prior service cost (credit) 0 0  
Accumulated other comprehensive loss (gain) 140.5 162.8  
Defined Benefit Plan, Accumulated Benefit Obligation 314.7 332.7  
Pension Benefits, Foreign [Member]
      
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]      
Defined Benefit Plan, Settlements, Plan Assets 0 0  
Change in benefit obligation:      
Benefit obligation at beginning of year 86.1 75.0  
Service cost 0 1.3 1.9
Interest cost 3.7 3.9 4.3
Defined Benefit Plan, Curtailments 0 0  
Defined Benefit Plan, Recognized Net Gain (Loss) Due to Settlements 0 0  
Foreign exchange impact (1.2) (5.5)  
Actuarial (gain)/loss 4.5 12.8  
Employee contributions 0 0.3  
Benefits paid (1.9) (1.7)  
Benefit obligation at end of year 91.2 86.1 75.0
Change in plan assets:      
Fair value of plan assets at beginning of year 72.6 69.0  
Actual return on plan assets 11.1 (3.9)  
Foreign exchange impact (1.2) (4.9)  
Employer contributions 3.6 13.8  
Employee contributions 0 0.3  
Benefits paid (1.9) (1.7)  
Fair value of plan assets at end of year 84.2 72.6 69.0
Funded status:      
Under funded status at end of year (7.0) (13.5)  
The components of the amounts recognized in the Consolidated Balance Sheets are as follows.      
Current liabilities 0 0  
Non-current liabilities (7.0) (13.5)  
The components of the amounts recognized in accumulated other comprehensive loss before the effect of income taxes are as follows.      
Unrecognized net actuarial loss 27.9 31.3  
Unrecognized prior service cost (credit) 0 0  
Accumulated other comprehensive loss (gain) 27.9 31.3  
Defined Benefit Plan, Accumulated Benefit Obligation 88.3 83.3  
Post-Retirement Benefits [Member]
      
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]      
Defined Benefit Plan, Settlements, Plan Assets 0 0  
Change in benefit obligation:      
Benefit obligation at beginning of year 9.8 10.3  
Service cost 0 0 0
Interest cost 0.3 0.4 0.5
Defined Benefit Plan, Curtailments 0 0  
Defined Benefit Plan, Recognized Net Gain (Loss) Due to Settlements 0 0  
Foreign exchange impact 0 0  
Actuarial (gain)/loss (0.2) 0  
Employee contributions 0 0  
Benefits paid (0.9) (0.9)  
Benefit obligation at end of year 9.0 9.8 10.3
Change in plan assets:      
Fair value of plan assets at beginning of year 0 0  
Actual return on plan assets 0 0  
Foreign exchange impact 0 0  
Employer contributions 0.9 0.9  
Employee contributions 0 0  
Benefits paid (0.9) (0.9)  
Fair value of plan assets at end of year 0 0 0
Funded status:      
Under funded status at end of year (9.0) (9.8)  
The components of the amounts recognized in the Consolidated Balance Sheets are as follows.      
Current liabilities (1.0) (1.1)  
Non-current liabilities (8.0) (8.7)  
The components of the amounts recognized in accumulated other comprehensive loss before the effect of income taxes are as follows.      
Unrecognized net actuarial loss 1.3 1.6  
Unrecognized prior service cost (credit) 0 0.1  
Accumulated other comprehensive loss (gain) $ 1.3 $ 1.7