Employee Benefit Plans (Narrative) (Details) - USD ($)	12 Months Ended
	Jun. 02, 2018	Jun. 03, 2017	May 28, 2016
Defined Benefit Plan Disclosure [Line Items]
Medical claim, maximum per occurrence	$ 225,000
Medical plan expense	16,100,000	$ 14,000,000	$ 11,800,000
Liability recorded for incurred but not reported claims	$ 1,100,000	900,000
Deferred compensation agreement, amount of years required for payment	65 years
Payments made under plan	$ 110,000	110,000	102,000
Liability related to deferred compensation agreements	1,500,000	1,600,000
Deferred compensation expense	693,000	616,000	347,000
Postretirement expense liability	2,300,000
2006 Plan
Defined Benefit Plan Disclosure [Line Items]
Payments made under plan	42,000	147,000
Liability related to deferred compensation agreements	3,100,000	2,500,000
Awards issued under deferred compensation plan	$ 298,000	$ 290,000	$ 284,000
KSOP
Defined Benefit Plan Disclosure [Line Items]
Company matching contribution percentage	3.00%	3.00%	3.00%
Company cash contribution	$ 3,300,000	$ 3,200,000	$ 2,900,000