Employee Benefit Plans (Narrative) (Details) - USD ($)	12 Months Ended
	Jun. 01, 2019	Jun. 02, 2018	Jun. 03, 2017
Defined Benefit Plan Disclosure [Line Items]
Medical claim, maximum per occurrence	$ 225,000
Medical plan expense	18,100,000	$ 16,100,000	$ 14,000,000.0
Liability recorded for incurred but not reported claims	$ 1,100,000
Deferred compensation agreement, amount of years required for payment	65 years
Payments made under plan	$ 129,000	110,000	110,000
Liability related to deferred compensation agreements	1,500,000	1,500,000
Deferred compensation expense	377,000	693,000	616,000
Postretirement expense liability	2,900,000	2,300,000
2006 Plan
Defined Benefit Plan Disclosure [Line Items]
Payments made under plan	84,000	42,000
Liability related to deferred compensation agreements	3,400,000	3,100,000
Awards issued under deferred compensation plan	$ 267,000	$ 298,000	$ 290,000
KSOP
Defined Benefit Plan Disclosure [Line Items]
Company matching contribution percentage	3.00%	3.00%	3.00%
Company cash contribution	$ 3,700,000	$ 3,300,000	$ 3,200,000