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Income Taxes - Schedule of Components of Income Tax Expense (Benefit) (Details) - USD ($)
$ in Millions
 12 Months Ended
Jun. 01, 2024
Jun. 03, 2023
May 28, 2022
Income Tax Disclosure [Abstract]      
Domestic - Federal $ 10.8 $ 4.2 $ (3.8)
Domestic - State 7.4 2.2 0.2
Foreign 34.6 42.3 38.1
Current income tax expense (benefit) 52.8 48.7 34.5
Domestic - Federal (22.2) (32.5) (12.2)
Domestic - State (6.5) (4.4) (5.0)
Foreign (9.4) (7.3) (6.2)
Deferred income tax expense (benefit) (38.1) (44.2) (23.4)
Income tax expense $ 14.7 $ 4.5 $ 11.1