Fair Value Measurements - Fair Value Hierarchy (Details) - USD ($) $ in Millions	Sep. 02, 2017	Jun. 03, 2017
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Available-for-sale marketable securities	$ 8.7	$ 8.6
Interest rate swap agreement	2.6
Interest rate swap agreement	1.7
Fixed Income Securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Available-for-sale marketable securities	7.8	7.7
Mutual funds - equity
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Available-for-sale marketable securities	0.9	0.9
Fair Value, Inputs, Level 2 \| Fair Value, Measurements, Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Deferred compensation plan	13.5	12.8
Total	25.3	25.2
Contingent consideration	0.0	0.0
Total	2.1	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
Foreign currency forward contracts	0.5	0.5
Foreign currency forward contracts	0.4	0.6
Fair Value, Inputs, Level 2 \| Fair Value, Measurements, Recurring \| Interest Rate Swap [Member]
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Interest rate swap agreement	2.6	3.3
Interest rate swap agreement	1.7	0.0
Fair Value, Inputs, Level 2 \| Fair Value, Measurements, Recurring \| Fixed Income Securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Available-for-sale marketable securities	7.8	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
Available-for-sale marketable securities	0.9	0.9
Fair Value, Inputs, Level 3 \| Fair Value, Measurements, Recurring
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	0.5	0.5
Total	0.5	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
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 [Member]
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis
Interest rate swap agreement	0.0	0.0
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
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
Available-for-sale marketable securities	$ 0.0	$ 0.0

Fair value portion of probable future economic benefits obtained or controlled by an entity as a result of past transactions or events.

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

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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
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Amount of liability recognized arising from contingent consideration in a business combination.

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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
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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/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
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No definition available.

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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.

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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
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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.

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