Fair Value - Schedule of Fair Value Assets and Liabilities Measured on a Recurring and Nonrecurring Basis (Details) - Fair Value, Recurring - USD ($) $ in Millions	Jun. 01, 2024	Jun. 03, 2023
NAV
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Deferred compensation plan	$ 0.0	$ 0.0
Total	17.5	17.3
Total	0.0	0.0
Total	17.5	17.3
Total	0.0	0.0
NAV \| Foreign currency forward contracts
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Foreign currency forward contracts - asset	0.0	0.0
Foreign currency forward contracts - liability	0.0	0.0
Quoted Prices with Other Observable Inputs (Level 2)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Deferred compensation plan	19.1	16.3
Total	20.2	17.6
Total	0.4	1.8
Total	20.2	17.6
Total	0.4	1.8
Quoted Prices with Other Observable Inputs (Level 2) \| Foreign currency forward contracts
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Foreign currency forward contracts - asset	1.1	1.3
Foreign currency forward contracts - liability	0.4	1.8
Quoted Prices with Other Observable Inputs (Level 2) \| Other Comprehensive Income (Loss)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Total	61.7	59.9
Total	0.0	3.0
Total	61.7	59.9
Total	0.0	3.0
Quoted Prices with Other Observable Inputs (Level 2) \| Other Comprehensive Income (Loss) \| Interest rate swap agreement
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Interest rate swap agreement - asset	61.7	59.9
Interest rate swap agreement - liability	0.0	3.0
Money Market Funds \| NAV
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Money market funds	17.5	17.3
Money Market Funds \| Quoted Prices with Other Observable Inputs (Level 2)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Money market funds	$ 0.0	$ 0.0

Fair value portion of asset recognized for present right to economic benefit.

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 820
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Fair value portion of currency on hand as well as demand deposits with banks or financial institutions. Includes other kinds of accounts that have the general characteristics of demand deposits. Also includes short-term, highly liquid investments that are both readily convertible to known amounts of cash and so near their maturity that they present insignificant risk of changes in value because of changes in interest rates.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 820
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-Name Accounting Standards Codification
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Carrying amount as of the balance sheet date of assets held under deferred compensation agreements.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 210
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Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

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Fair value portion of asset contracts related to the exchange of different currencies, including, but not limited to, foreign currency options, forward contracts, and swaps.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 820
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Fair value portion of liability contracts related to the exchange of different currencies, including, but not limited to, foreign currency options, forward (delivery or nondelivery) contracts, and swaps entered into.

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Fair value as of the balance sheet date of all interest rate derivative assets designated as cash flow hedging instruments.

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Fair value as of the balance sheet date of all interest rate derivative liabilities designated as cash flow hedging instruments.

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Fair value of financial and nonfinancial obligations.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
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