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Fair Value of Financial Instruments - Schedule of Fair Value Assets and Liabilities Measured on a Recurring and Nonrecurring Basis (Details) £ in Millions, $ in Millions | Jun. 01, 2019 USD ($) | Jun. 01, 2019 GBP (£) | Jun. 02, 2018 USD ($) | Jun. 02, 2018 GBP (£) | Jun. 12, 2017 USD ($) | Sep. 13, 2016 USD ($)
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Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis |  |  |  |  |  |
Available-for-sale Securities, Amortized Cost Basis | $ 8.7 |  | $ 8.5 |  |  |
Available-for-sale Securities | 8.8 |  | 8.6 |  |  |
Interest rate swap agreement - asset | £ |  | £ 19.2 |  | £ 19.9 |  |
Interest rate swap agreement - liability | 38.1 |  | 37.3 |  |  |
Interest rate swap agreement |  |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis |  |  |  |  |  |
Interest rate swap agreement - asset |  |  |  |  | $ 75.0 | $ 150.0
Mutual funds - equity |  |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis |  |  |  |  |  |
Available-for-sale Securities, Amortized Cost Basis | 0.8 |  | 0.7 |  |  |
Available-for-sale Securities | 0.9 |  | 0.9 |  |  |
Mutual funds - fixed income |  |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis |  |  |  |  |  |
Available-for-sale Securities, Amortized Cost Basis |  |  | 7.8 |  |  |
Available-for-sale Securities | 7.9 |  | 7.7 |  |  |
Fair Value, Measurements, Recurring [Member] |  |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis |  |  |  |  |  |
Total |  |  | 16.4 |  |  |
NAV | Fair Value, Measurements, Recurring [Member] |  |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis |  |  |  |  |  |
Total | 69.5 |  | 121.0 |  |  |
Quoted Prices With Other Observable Inputs (Level 2) | Fair Value, Measurements, Recurring [Member] |  |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis |  |  |  |  |  |
Deferred compensation plan | 12.5 |  | 15.1 |  |  |
Total | 13.4 |  |  |  |  |
Contingent consideration | 0.0 |  | 0.0 |  |  |
Total | 1.4 |  | 0.3 |  |  |
Quoted Prices With Other Observable Inputs (Level 2) | Fair Value, Measurements, Recurring [Member] | Interest rate swap agreement |  |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis |  |  |  |  |  |
Interest Rate Cash Flow Hedge Asset at Fair Value | (1.2) |  |  |  |  |
Interest rate swap agreement - liability |  |  | 0.0 |  |  |
Quoted Prices With Other Observable Inputs (Level 2) | Fair Value, Measurements, Recurring [Member] | Mutual funds - equity |  |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis |  |  |  |  |  |
Mutual funds - equity | 0.9 |  | 0.9 |  |  |
Quoted Prices With Other Observable Inputs (Level 2) | Fair Value, Measurements, Recurring [Member] | Mutual funds - fixed income |  |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis |  |  |  |  |  |
Available-for-sale Securities, Amortized Cost Basis | 7.9 |  |  |  |  |
Available-for-sale Securities |  |  | 7.7 |  |  |
Management Estimates (Level 3) | Fair Value, Measurements, Recurring [Member] |  |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis |  |  |  |  |  |
Deferred compensation plan | 0.0 |  | 0.0 |  |  |
Total | 0.0 |  | 0.0 |  |  |
Contingent consideration | 0.2 |  | 0.5 |  |  |
Total | 0.2 |  | 0.5 |  |  |
Management Estimates (Level 3) | Fair Value, Measurements, Recurring [Member] | 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 |  |  |
Management Estimates (Level 3) | Fair Value, Measurements, Recurring [Member] | Interest rate swap agreement |  |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis |  |  |  |  |  |
Interest rate swap agreement - asset | 0.0 |  | 0.0 |  |  |
Interest rate swap agreement - liability | 0.0 |  | 0.0 |  |  |
Management Estimates (Level 3) | Fair Value, Measurements, Recurring [Member] | Mutual funds - equity |  |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis |  |  |  |  |  |
Mutual funds - equity | 0.0 |  | 0.0 |  |  |
Management Estimates (Level 3) | Fair Value, Measurements, Recurring [Member] | Mutual funds - fixed income |  |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis |  |  |  |  |  |
Available-for-sale Securities | 0.0 |  | 0.0 |  |  |
Money Market Funds | NAV | Fair Value, Measurements, Recurring [Member] |  |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis |  |  |  |  |  |
Money market funds | 69.5 |  | 121.0 |  |  |
Money Market Funds | Quoted Prices With Other Observable Inputs (Level 2) | Fair Value, Measurements, Recurring [Member] |  |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis |  |  |  |  |  |
Money market funds | 0.0 |  | 0.0 |  |  |
Money Market Funds | Management Estimates (Level 3) | Fair Value, Measurements, Recurring [Member] |  |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis |  |  |  |  |  |
Money market funds | 0.0 |  | 0.0 |  |  |
Other Current Assets | Quoted Prices With Other Observable Inputs (Level 2) | Fair Value, Measurements, Recurring [Member] | Foreign currency forward contracts |  |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis |  |  |  |  |  |
Foreign currency forward contracts - asset | 0.0 |  | 0.4 |  |  |
Other Current Liabilities | Quoted Prices With Other Observable Inputs (Level 2) | Fair Value, Measurements, Recurring [Member] | Foreign currency forward contracts |  |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis |  |  |  |  |  |
Foreign currency forward contracts - liability | 1.4 |  | 0.3 |  |  |
Other Assets | Quoted Prices With Other Observable Inputs (Level 2) | Fair Value, Measurements, Recurring [Member] |  |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis |  |  |  |  |  |
Available-for-sale Securities | 8.9 |  | 22.7 |  |  |
Other Assets | Management Estimates (Level 3) | Fair Value, Measurements, Recurring [Member] |  |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis |  |  |  |  |  |
Available-for-sale Securities | 0.0 |  | 0.0 |  |  |
Other Liabilities | Quoted Prices With Other Observable Inputs (Level 2) | Fair Value, Measurements, Recurring [Member] |  |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis |  |  |  |  |  |
Available-for-sale Securities | 2.2 |  | 0.0 |  |  |
Other Liabilities | Management Estimates (Level 3) | Fair Value, Measurements, Recurring [Member] |  |  |  |  |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis |  |  |  |  |  |
Available-for-sale Securities | $ 0.0 |  | $ 0.0 |  |  |

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