Significant Accounting Policies (Narrative) (Details) - USD ($) $ in Thousands	12 Months Ended
	May 30, 2020	Jun. 01, 2019	Jun. 02, 2018
Significant Accounting Policies [Line Items]
Checks outstanding in excess of related book cash balances	$ 11,200	$ 6,200
Allowance for doubtful accounts	744	206
Delivery costs	52,200	53,600	$ 53,200
Advertising expense	$ 6,000	$ 7,300	$ 6,300
Two Affiliated Customers | Sales Revenue, Net
Significant Accounting Policies [Line Items]
Concentration risk, percentage	32.10%	33.70%	33.20%
Two Affiliated Customers | Accounts Receivable
Significant Accounting Policies [Line Items]
Concentration risk, percentage	29.50%	29.60%
Minimum
Significant Accounting Policies [Line Items]
Finance lease, remaining terms	1 month
Intangible assets estimated useful life	5 years
Maximum
Significant Accounting Policies [Line Items]
Finance lease, remaining terms	5 years
Intangible assets estimated useful life	15 years
Buildings and improvements | Minimum
Significant Accounting Policies [Line Items]
Property, plant and equipment useful life	15 years
Buildings and improvements | Maximum
Significant Accounting Policies [Line Items]
Property, plant and equipment useful life	25 years
Machinery and equipment | Minimum
Significant Accounting Policies [Line Items]
Property, plant and equipment useful life	3 years
Machinery and equipment | Maximum
Significant Accounting Policies [Line Items]
Property, plant and equipment useful life	12 years
Building | Minimum
Significant Accounting Policies [Line Items]
Initial operating lease terms	3 years
Building | Maximum
Significant Accounting Policies [Line Items]
Initial operating lease terms	10 years
Trucks | Minimum
Significant Accounting Policies [Line Items]
Initial operating lease terms	5 years
Trucks | Maximum
Significant Accounting Policies [Line Items]
Initial operating lease terms	7 years