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Accumulated Other Comprehensive Loss (Details) - USD ($)
$ in Thousands
 12 Months Ended
May 29, 2021
May 30, 2020
Jun. 01, 2019
Increase (Decrease) in Stockholders' Equity [Roll Forward]      
Accumulated other comprehensive income (loss) - beginning balance $ 643,000    
Other comprehensive income (loss) before reclassification (net of tax)     $ (12,800)
Accumulated other comprehensive income (loss) - ending balance 849,600 $ 643,000  
Cumulative Translation Adjustments      
Increase (Decrease) in Stockholders' Equity [Roll Forward]      
Accumulated other comprehensive income (loss) - beginning balance (56,000) (48,300) (34,100)
Net current period other comprehensive income (loss) 52,100 (7,700) (14,200)
Accumulated other comprehensive income (loss) - ending balance (3,900) (56,000) (48,300)
Pension and Other Post-Retirement Benefit Plans      
Increase (Decrease) in Stockholders' Equity [Roll Forward]      
Accumulated other comprehensive income (loss) - beginning balance (59,200) (45,000) (37,200)
Other comprehensive income (loss) before reclassification (net of tax) 5,300 (16,900) (10,000)
Reclassification from accumulated other comprehensive income - Other, net 5,500 3,300 2,600
Tax (expense) benefit (2,000) (600) (400)
Net reclassifications 3,500 2,700 2,200
Net current period other comprehensive income (loss) 8,800 (14,200) (7,800)
Accumulated other comprehensive income (loss) - ending balance (50,400) (59,200) (45,000)
Other comprehensive income (loss) before reclassifications, tax (30) 3,500 2,000
Interest Rate Swap Agreement      
Increase (Decrease) in Stockholders' Equity [Roll Forward]      
Accumulated other comprehensive income (loss) - beginning balance (18,900) (900) 9,900
Other comprehensive income (loss) before reclassification (net of tax) 12,600 (17,200)  
Other comprehensive income (loss) before reclassification (net of tax)     (12,800)
Reclassification from accumulated other comprehensive income - Other, net (4,500) (800) 500
Net reclassifications (4,500) (800) 500
Net current period other comprehensive income (loss) 8,100 (18,000) (12,300)
Accumulated other comprehensive income (loss) - ending balance (10,800) (18,900) (900)
Other comprehensive income (loss) before reclassifications, tax (2,600) 5,800 5,300
Unrealized Gains on Securities      
Increase (Decrease) in Stockholders' Equity [Roll Forward]      
Accumulated other comprehensive income (loss) - beginning balance 100 0 100
Other comprehensive income (loss) before reclassification (net of tax) (100) 100 0
Accumulated other comprehensive income (loss) - ending balance 0 100 0
Accumulated Other Comprehensive Income (Loss)      
Increase (Decrease) in Stockholders' Equity [Roll Forward]      
Accumulated other comprehensive income (loss) - beginning balance (134,000) (94,200)  
Accumulated other comprehensive income (loss) - ending balance $ (65,100) $ (134,000) (94,200)
Cumulative effect of accounting changes | Interest Rate Swap Agreement      
Increase (Decrease) in Stockholders' Equity [Roll Forward]      
Accumulated other comprehensive income (loss) - beginning balance     1,500
Cumulative effect of accounting changes | Unrealized Gains on Securities      
Increase (Decrease) in Stockholders' Equity [Roll Forward]      
Accumulated other comprehensive income (loss) - beginning balance     $ (100)