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Fair Value Measurements - Fair Value Hierarchy (Details) - USD ($) $ in Millions | Mar. 03, 2018 | Jun. 03, 2017
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Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |
Available-for-sale marketable securities | $ 8.4 | $ 8.6
Fixed Income Securities |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |
Available-for-sale marketable securities | 7.6 | 7.7
Mutual funds - equity |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |
Available-for-sale marketable securities | 0.8 | 0.9
Fair Value, Inputs, Level 2 | Fair Value, Measurements, Recurring |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |
Deferred compensation plan | 11.7 | 12.8
Total | 135.7 | 25.2
Contingent consideration | 0.0 | 0.0
Total | 0.6 | 0.6
Fair Value, Inputs, Level 2 | Fair Value, Measurements, Recurring | Foreign Exchange Forward |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |
Foreign currency forward contracts | 0.5 | 0.5
Foreign currency forward contracts | 0.6 | 0.6
Fair Value, Inputs, Level 2 | Fair Value, Measurements, Recurring | Interest Rate Swap |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |
Interest rate swap agreement | 13.7 | 3.3
Fair Value, Inputs, Level 2 | Fair Value, Measurements, Recurring | Fixed Income Securities |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |
Available-for-sale marketable securities | 7.6 | 7.7
Fair Value, Inputs, Level 2 | Fair Value, Measurements, Recurring | Mutual funds - equity |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |
Available-for-sale marketable securities | 0.8 | 0.9
Fair Value, Inputs, Level 3 | Fair Value, Measurements, Recurring |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |
Deferred compensation plan | 0.0 | 0.0
Total | 0.0 | 0.0
Contingent consideration | 0.4 | 0.5
Total | 0.4 | 0.5
Fair Value, Inputs, Level 3 | Fair Value, Measurements, Recurring | Foreign Exchange Forward |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |
Foreign currency forward contracts | 0.0 | 0.0
Foreign currency forward contracts | 0.0 | 0.0
Fair Value, Inputs, Level 3 | Fair Value, Measurements, Recurring | Interest Rate Swap |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |
Interest rate swap agreement | 0.0 | 0.0
Fair Value, Inputs, Level 3 | Fair Value, Measurements, Recurring | Fixed Income Securities |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |
Available-for-sale marketable securities | 0.0 | 0.0
Fair Value, Inputs, Level 3 | Fair Value, Measurements, Recurring | Mutual funds - equity |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |
Available-for-sale marketable securities | 0.0 | 0.0
Money Market Funds [Member] | Fair Value, Inputs, Level 2 | Fair Value, Measurements, Recurring |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |
Money Market Funds, at Carrying Value | 31.4 | 0.0
Money Market Funds [Member] | Fair Value, Inputs, Level 3 | Fair Value, Measurements, Recurring |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |
Money Market Funds, at Carrying Value | 0.0 | 0.0
Commercial Paper [Member] | Fair Value, Inputs, Level 2 | Fair Value, Measurements, Recurring |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |
Commercial Paper | 70.0 | 0.0
Commercial Paper [Member] | Fair Value, Inputs, Level 3 | Fair Value, Measurements, Recurring |  |
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items] |  |
Commercial Paper | $ 0.0 | $ 0.0

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- Definition Fair value portion of probable future economic benefits obtained or controlled by an entity as a result of past transactions or events. + References Reference 1: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 820 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (a) -URI http://asc.fasb.org/extlink&oid=66048111&loc=d3e19207-110258 + Details
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- Definition Amount of investment in debt and equity securities categorized neither as held-to-maturity nor trading. + References Reference 1: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 320 -SubTopic 10 -Section 25 -Paragraph 1 -Subparagraph (b) -URI http://asc.fasb.org/extlink&oid=65884222&loc=d3e22054-111558 Reference 2: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 320 -SubTopic 10 -Section 50 -Paragraph 5 -Subparagraph (aa) -URI http://asc.fasb.org/extlink&oid=73527792&loc=d3e27232-111563 Reference 3: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 320 -SubTopic 10 -Section 45 -Paragraph 1 -URI http://asc.fasb.org/extlink&oid=66010992&loc=d3e26610-111562 + Details
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- Definition Amount of liability recognized arising from contingent consideration in a business combination. + References Reference 1: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 805 -SubTopic 30 -Section 50 -Paragraph 1 -Subparagraph (c) -URI http://asc.fasb.org/extlink&oid=35744584&loc=d3e6927-128479 Reference 2: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 805 -SubTopic 30 -Section 35 -Paragraph 1 -Subparagraph (b) -URI http://asc.fasb.org/extlink&oid=6911338&loc=d3e6819-128478 Reference 3: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 805 -SubTopic 30 -Section 25 -Paragraph 6 -URI http://asc.fasb.org/extlink&oid=6911189&loc=d3e6408-128476 + Details
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- Definition Carrying value as of the balance sheet date of short-term borrowings using unsecured obligations issued by banks, corporations and other borrowers to investors. The maturities of these money market securities generally do not exceed 270 days. + References Reference 1: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 210 -SubTopic 10 -Section S99 -Paragraph 1 -Subparagraph (SX 210.5-02(19)(a)(3)) -URI http://asc.fasb.org/extlink&oid=6877327&loc=d3e13212-122682 Reference 2: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 944 -SubTopic 210 -Section S99 -Paragraph 1 -Subparagraph (SX 210.7-03(a)(16)) -URI http://asc.fasb.org/extlink&oid=6879938&loc=d3e572229-122910 Reference 3: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 942 -SubTopic 210 -Section S99 -Paragraph 1 -Subparagraph (SX 210.9-03(13)(2)) -URI http://asc.fasb.org/extlink&oid=6876686&loc=d3e534808-122878 + Details
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- Definition Carrying amount as of the balance sheet date of assets held under deferred compensation agreements. + References Reference 1: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 210 -SubTopic 10 -Section S99 -Paragraph 1 -Subparagraph (SX 210.5-02.17) -URI http://asc.fasb.org/extlink&oid=6877327&loc=d3e13212-122682 + Details
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- Definition 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. + References No definition available. + Details
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- Definition 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 No definition available. + Details
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- Definition Fair value as of the balance sheet date of all interest rate derivative assets designated as cash flow hedging instruments. + References Reference 1: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 815 -SubTopic 10 -Section 50 -Paragraph 4B -Subparagraph (c)(1) -URI http://asc.fasb.org/extlink&oid=64837297&loc=SL5624163-113959 + Details
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- Definition Fair value of financial and nonfinancial obligations. + References Reference 1: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Topic 820 -SubTopic 10 -Section 50 -Paragraph 2 -Subparagraph (a) -URI http://asc.fasb.org/extlink&oid=66048111&loc=d3e19207-110258 + Details
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- Definition Investment in short-term money-market instruments (such as commercial paper, banker's acceptances, repurchase agreements, government securities, certificates of deposit, and so forth) which are highly liquid (that is, readily convertible to known amounts of cash) and so near their maturity that they present an insignificant risk of changes in value because of changes in interest rates. Generally, only investments with original maturities of three months or less qualify as cash equivalents by definition. Original maturity means an original maturity to the entity holding the investment. For example, both a three-month US Treasury bill and a three-year Treasury note purchased three months from maturity qualify as cash equivalents. However, a Treasury note purchased three-years ago does not become a cash equivalent when its remaining maturity is three months. + References Reference 1: http://www.xbrl.org/2003/role/presentationRef -Publisher FASB -Name Accounting Standards Codification -Glossary Cash Equivalents -URI http://asc.fasb.org/extlink&oid=6507016 + Details
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