Accumulated Other Comprehensive Loss (Details) - USD ($) $ in Millions	3 Months Ended				6 Months Ended
	Dec. 02, 2023	Sep. 02, 2023	Dec. 03, 2022	Sep. 03, 2022	Dec. 02, 2023	Dec. 03, 2022
Accumulated Other Comprehensive Income [Roll Forward]
Balance at beginning of period	$ 1,422.3	$ 1,432.6	$ 1,374.8	$ 1,427.1	$ 1,432.6	$ 1,427.1
Other comprehensive income (loss), net of tax before reclassifications					(4.0)	(8.8)
Reclassification from accumulated other comprehensive loss - Other, net					15.0	3.1
Tax benefit					0.0	(0.3)
Net reclassifications					15.0	2.8
Net current period other comprehensive income (loss)	(0.6)	11.6	51.8	(57.8)	11.0	(6.0)
Balance at end of period	1,420.6	1,422.3	1,434.3	1,374.8	1,420.6	1,434.3
Accumulated Other Comprehensive Loss
Accumulated Other Comprehensive Income [Roll Forward]
Balance at beginning of period	(83.5)	(95.1)	(164.9)	(107.1)	(95.1)	(107.1)
Net current period other comprehensive income (loss)	(0.6)	11.6	51.8	(57.8)
Balance at end of period	(84.1)	(83.5)	(113.1)	(164.9)	(84.1)	(113.1)
Cumulative Translation Adjustments
Accumulated Other Comprehensive Income [Roll Forward]
Balance at beginning of period		(114.0)		(93.9)	(114.0)	(93.9)
Other comprehensive income (loss), net of tax before reclassifications					11.2	(28.3)
Reclassification from accumulated other comprehensive loss - Other, net					0.0	0.0
Tax benefit					0.0	0.0
Net reclassifications					0.0	0.0
Net current period other comprehensive income (loss)					11.2	(28.3)
Balance at end of period	(102.8)		(122.2)		(102.8)	(122.2)
Pension and Other Post-retirement Benefit Plans
Accumulated Other Comprehensive Income [Roll Forward]
Balance at beginning of period		(23.8)		(36.9)	(23.8)	(36.9)
Other comprehensive income (loss), net of tax before reclassifications					0.0	0.0
Reclassification from accumulated other comprehensive loss - Other, net					(0.1)	1.1
Tax benefit					0.0	(0.3)
Net reclassifications					(0.1)	0.8
Net current period other comprehensive income (loss)					(0.1)	0.8
Balance at end of period	(23.9)		(36.1)		(23.9)	(36.1)
Interest Rate Swap Agreement
Accumulated Other Comprehensive Income [Roll Forward]
Balance at beginning of period		$ 42.7		$ 23.7	42.7	23.7
Other comprehensive income (loss), net of tax before reclassifications					(15.2)	19.5
Reclassification from accumulated other comprehensive loss - Other, net					15.1	2.0
Tax benefit					0.0	0.0
Net reclassifications					15.1	2.0
Net current period other comprehensive income (loss)					(0.1)	21.5
Balance at end of period	$ 42.6		$ 45.2		$ 42.6	$ 45.2