Employee Benefit Plans (Narrative) (Details) - USD ($)		12 Months Ended
	Jul. 10, 2018	May 30, 2020	Jun. 01, 2019	Jun. 02, 2018
Defined Benefit Plan Disclosure [Line Items]
Medical claim, maximum per occurrence		$ 225,000
Medical plan expense		17,800,000	$ 18,100,000	$ 16,100,000
Liability recorded for incurred but not reported claims		$ 1,700,000	1,100,000
Deferred compensation agreement, amount of years required for payment		65 years
Payments made under plan		$ 150,000	129,000	110,000
Liability related to deferred compensation agreements		1,400,000	1,500,000
Deferred compensation expense		621,000	377,000	693,000
Postretirement expense liability		3,400,000	2,900,000
Revolving Credit Facility | Line of Credit
Defined Benefit Plan Disclosure [Line Items]
Debt instrument, term	5 years
2006 Plan
Defined Benefit Plan Disclosure [Line Items]
Payments made under plan		1,200,000	84,000
Liability related to deferred compensation agreements		2,700,000	3,400,000
Awards issued under deferred compensation plan		266,000	267,000	$ 298,000
KSOP
Defined Benefit Plan Disclosure [Line Items]
Company matching contribution percentage				3.00%
Company cash contribution		$ 3,800,000	$ 3,700,000	$ 3,300,000