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Accumulated Other Comprehensive Loss (Details) - USD ($)
$ in Millions
 12 Months Ended
May 30, 2020
Jun. 01, 2019
Jun. 02, 2018
Jun. 03, 2018
Cumulative translation adjustments [Roll Forward]        
Cumulative translation adjustments at beginning of period $ (48.3) $ (34.1) $ (36.8)  
Other comprehensive (loss) income (7.7) (14.2) 2.7  
Balance at end of period (56.0) (48.3) (34.1)  
Pension and other post-retirement benefit plans [Roll Forward]        
Pension and other post-retirement benefit plans at beginning of period (45.0) (37.2) 47.6  
Other comprehensive (loss) income before reclassifications (net of tax of $3.5, $2.0, and($2.9)) 16.9 10.0 (5.3)  
Net reclassifications 2.7 2.2 5.1  
Other Comprehensive Income (Loss), Net of Tax 39.8 34.3 (20.9)  
Balance at end of period (59.2) (45.0) (37.2)  
Interest rate swap agreement [Roll Forward]        
Interest rate swap agreement at beginning of period (0.9) 9.9 2.1  
Cumulative effect of accounting change 683.9 712.7    
Other Comprehensive Income (Loss), before Reclassifications, Net of Tax (17.2) (12.8) 7.5  
Net reclassifications (0.8) 0.5 0.3  
Net current period other comprehensive (loss) income (18.0) (12.3) 7.8  
Balance at end of period (18.9) (0.9) 9.9  
Available for sale securities [Roll Forward]        
Unrealized holding gains on securities at beginning of period 0.0 0.1 0.1  
Cumulative effect of accounting change 683.9 712.7    
Other comprehensive income before reclassifications 0.1 0.0 0.0  
Balance at end of period 0.1 0.0 0.1  
Total Accumulated other comprehensive loss (134.0) (94.2) (61.3)  
Other, net        
Pension and other post-retirement benefit plans [Roll Forward]        
Reclassification from accumulated other comprehensive income - Other, net 3.3 2.6 4.2  
Accumulated Defined Benefit Plans Adjustment Attributable to Parent [Member]        
Pension and other post-retirement benefit plans [Roll Forward]        
Tax (expense) benefit (0.6) (0.4) 0.9  
Other Comprehensive Income (Loss), Net of Tax (14.2) (7.8) 10.4  
Accumulated Net Gain (Loss) from Cash Flow Hedges Attributable to Parent | Other, net        
Interest rate swap agreement [Roll Forward]        
Reclassification from Accumulated Other Comprehensive Income, Current Period, before Tax $ (0.8) $ 0.5 $ 0.3  
Accounting Standards Update 2018-02        
Interest rate swap agreement [Roll Forward]        
Cumulative effect of accounting change       $ 1.5
Available for sale securities [Roll Forward]        
Cumulative effect of accounting change       1.5
Accounting Standards Update 2016-01        
Interest rate swap agreement [Roll Forward]        
Cumulative effect of accounting change       (0.1)
Available for sale securities [Roll Forward]        
Cumulative effect of accounting change       $ (0.1)