Fair Value Measurements (Tables)	3 Months Ended
Sep. 02, 2023
Fair Value Disclosures [Abstract]
Schedule of Long-term Debt Instruments	The carrying value and fair value of the Company's long-term debt, including current maturities, is as follows for the periods indicated:(In millions)September 2, 2023June 3, 2023Carrying value$1,350.1 $1,414.4 Fair value$1,364.0 $1,378.2
Schedule of Assets and Liabilities Measured at Fair Value and Recorded in Net Earnings	The following table sets forth financial assets and liabilities measured at fair value through net income and the respective pricing levels to which the fair value measurements are classified within the fair value hierarchy as of September 2, 2023 and June 3, 2023. (In millions)September 2, 2023June 3, 2023Financial AssetsNAVQuoted Prices with OtherObservable Inputs (Level 2)NAVQuoted Prices with Other Observable Inputs (Level 2)Cash equivalents:Money market funds$4.2 $— $17.3 $— Foreign currency forward contracts— 0.6 — 1.3 Deferred compensation plan— 18.0 — 16.3 Total$4.2 $18.6 $17.3 $17.6 Financial LiabilitiesForeign currency forward contracts— 1.3 — 1.8 Total$— $1.3 $— $1.8 The following table sets forth financial assets and liabilities measured at fair value through other comprehensive income and the respective pricing levels to which the fair value measurements are classified within the fair value hierarchy as of September 2, 2023 and June 3, 2023. (In millions)September 2, 2023June 3, 2023Financial AssetsBalance Sheet LocationQuoted Prices with Other Observable Inputs (Level 2)Quoted Prices with Other Observable Inputs (Level 2)Interest rate swap agreementOther noncurrent assets$67.2 $59.9 Total$67.2 $59.9 Financial LiabilitiesInterest rate swap agreementOther liabilities$— $3.0 Total$— $3.0
Schedule of Interest Rate Derivatives	(In millions)Notional AmountForward Start DateAmendment Effective DateTermination DateEffective Fixed Interest RateSeptember 2016 Interest Rate Swap$150.0 January 3, 2018February 3, 2023January 3, 20281.910 %June 2017 Interest Rate Swap$75.0 January 3, 2018February 3, 2023January 3, 20282.348 %January 2022 Interest Rate Swap$575.0 January 31, 2022January 31, 2023January 29, 20271.650 %March 2023 Interest Rate Swap$150.0 March 3, 2023noneJanuary 3, 20293.950 %The following table summarizes the effects of the interest rate swap agreements for the three months ended:Three Months Ended(In millions)September 2, 2023September 3, 2022Gain recognized in Other comprehensive loss (effective portion)$7.8 $14.3 Gain (Loss) reclassified from Accumulated other comprehensive loss into earnings$7.4 $(0.4)
Schedule of Redeemable Noncontrolling Interest	Changes in the Company's redeemable noncontrolling interest in HAY for the three months ended September 2, 2023 and September 3, 2022 are as follows:(In millions)September 2, 2023September 3, 2022Beginning Balance$107.6 $106.9 Net income attributable to redeemable noncontrolling interests(0.6)1.6 Dividend attributable to redeemable noncontrolling interests— — Cumulative translation adjustments attributable to redeemable noncontrolling interests— 0.1 Foreign currency translation adjustments0.6 (7.9)Ending Balance$107.6 $100.7

Tabular disclosure of the fair value of financial instruments, including financial assets and financial liabilities, and the measurements of those instruments, assets, and liabilities.

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 820
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482106/820-10-50-2

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 825
-SubTopic 10
-Section 50
-Paragraph 11
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482907/825-10-50-11

+ Details

Name:	us-gaap_FairValueByBalanceSheetGroupingTextBlock
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:textBlockItemType
Balance Type:	na
Period Type:	duration

- References

No definition available.

+ Details

Name:	us-gaap_FairValueDisclosuresAbstract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Tabular disclosure of redeemable noncontrolling interest (as defined) included in the statement of financial position as either a liability or temporary equity. As of the date of the statement of financial position, such redeemable noncontrolling interest is currently redeemable, as defined, for cash or other assets of the entity at (1) at a fixed or determinable price on a fixed or determinable date, (2) at the option of the holder of the noncontrolling interest, or (3) upon occurrence of an event that is not solely within the control of the entity.

+ References

No definition available.

+ Details

Name:	us-gaap_RedeemableNoncontrollingInterestTableTextBlock
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:textBlockItemType
Balance Type:	na
Period Type:	duration

- Definition

Tabular disclosure of assets and liabilities, including [financial] instruments measured at fair value that are classified in stockholders' equity, if any, that are measured at fair value on a recurring basis. The disclosures contemplated herein include the fair value measurements at the reporting date by the level within the fair value hierarchy in which the fair value measurements in their entirety fall, segregating fair value measurements using quoted prices in active markets for identical assets (Level 1), significant other observable inputs (Level 2), and significant unobservable inputs (Level 3).

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482106/820-10-50-2

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482106/820-10-50-2

+ Details

Name:	us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:textBlockItemType
Balance Type:	na
Period Type:	duration

- Definition

Tabular disclosure of interest rate derivatives, including, but not limited to, the fair value of the derivatives, statement of financial position location, and statement of financial performance location of these instruments.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 815
-SubTopic 10
-Section 50
-Paragraph 4C
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480434/815-10-50-4C

+ Details

Name:	us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:textBlockItemType
Balance Type:	na
Period Type:	duration