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Accumulated Other Comprehensive Loss (Details) - USD ($)
$ in Thousands
 12 Months Ended
Jun. 01, 2024
Jun. 03, 2023
May 28, 2022
Increase (Decrease) in Stockholders' Equity [Roll Forward]      
Balance at beginning of period $ 1,432,600 $ 1,427,100 $ 860,500
Net current period other comprehensive (loss) income 2,400 12,000 (42,000)
Balance at end of period 1,385,100 1,432,600 1,427,100
Cumulative Translation Adjustments      
Increase (Decrease) in Stockholders' Equity [Roll Forward]      
Balance at beginning of period (114,000) (93,900) (3,900)
Other comprehensive (loss) income before reclassifications 8,300 (20,100) (90,000)
Balance at end of period (105,700) (114,000) (93,900)
Pension and Other Post-Retirement Benefit Plans      
Increase (Decrease) in Stockholders' Equity [Roll Forward]      
Balance at beginning of period (23,800) (36,900) (50,400)
Other comprehensive (loss) income before reclassifications (9,100) 14,800 13,500
Reclassification from accumulated other comprehensive income - Other, net (300) 2,700 4,400
Tax expense (100) (4,400) (4,400)
Net reclassifications (400) (1,700) 0
Net current period other comprehensive (loss) income (9,500) 13,100 13,500
Balance at end of period (33,300) (23,800) (36,900)
Other comprehensive income (loss) before reclassifications, tax 1,600 (3,500) (20)
Interest Rate Swap Agreement      
Increase (Decrease) in Stockholders' Equity [Roll Forward]      
Balance at beginning of period 42,700 23,700 (10,800)
Other comprehensive (loss) income before reclassifications (27,100) 4,700 41,400
Reclassification from accumulated other comprehensive income - Other, net 30,700 14,300 (6,900)
Net reclassifications 30,700 14,300 (6,900)
Net current period other comprehensive (loss) income 3,600 19,000 34,500
Balance at end of period 46,300 42,700 23,700
Other comprehensive income (loss) before reclassifications, tax (1,200) (6,200) (11,600)
Accumulated Other Comprehensive (Loss) Income      
Increase (Decrease) in Stockholders' Equity [Roll Forward]      
Balance at beginning of period (95,100) (107,100) (65,100)
Net current period other comprehensive (loss) income 2,400 12,000 (42,000)
Balance at end of period $ (92,700) $ (95,100) $ (107,100)