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Accumulated Other Comprehensive Loss (Details) - USD ($)
$ in Thousands
 12 Months Ended
May 31, 2025
Jun. 01, 2024
Jun. 03, 2023
Increase (Decrease) in Stockholders' Equity [Roll Forward]      
Balance at beginning of period $ 1,385,100 $ 1,432,600 $ 1,427,100
Other comprehensive income (loss) 35,100 8,300 (20,100)
Net current period other comprehensive income (loss) 10,700 2,400 12,000
Balance at end of period 1,275,800 1,385,100 1,432,600
Cumulative Translation Adjustments      
Increase (Decrease) in Stockholders' Equity [Roll Forward]      
Balance at beginning of period (105,700) (114,000) (93,900)
Other comprehensive income (loss) 35,100 8,300 (20,100)
Balance at end of period (70,600) (105,700) (114,000)
Pension and Other Post-Retirement Benefit Plans      
Increase (Decrease) in Stockholders' Equity [Roll Forward]      
Balance at beginning of period (33,300) (23,800) (36,900)
Other comprehensive (loss) income before reclassifications (600) (9,100) 14,800
Reclassification from accumulated other comprehensive income - Other, net 4,000 (300) 2,700
Tax expense (1,000) (100) (4,400)
Net reclassifications 3,000 (400) (1,700)
Net current period other comprehensive income (loss) 2,400 (9,500) 13,100
Balance at end of period (30,900) (33,300) (23,800)
Other comprehensive income (loss) before reclassifications, tax 200 1,600 (3,500)
Interest Rate Swap Agreement      
Increase (Decrease) in Stockholders' Equity [Roll Forward]      
Balance at beginning of period 46,300 42,700 23,700
Other comprehensive (loss) income before reclassifications (52,200) (27,100) 4,700
Reclassification from accumulated other comprehensive income - Other, net 25,400 30,700 14,300
Net reclassifications 25,400 30,700 14,300
Net current period other comprehensive income (loss) (26,800) 3,600 19,000
Balance at end of period 19,500 46,300 42,700
Other comprehensive income (loss) before reclassifications, tax 8,800 (1,200) (6,200)
Accumulated Other Comprehensive (Loss) Income      
Increase (Decrease) in Stockholders' Equity [Roll Forward]      
Balance at beginning of period (92,700) (95,100) (107,100)
Net current period other comprehensive income (loss) 10,700 2,400 12,000
Balance at end of period $ (82,000) $ (92,700) $ (95,100)