LEASES - Additional Information (Details) $ in Thousands	12 Months Ended
	Jul. 29, 2023 USD ($) real_estate_partnership contract property	Jul. 30, 2022 USD ($)
Lessee, Lease, Description [Line Items]
Number of retail stores leased (in contracts) | contract	30
Lease renewal terms	5 years
Finance lease, right-of-use asset	$ 10,912	$ 11,859
Finance Lease, Right-of-Use Asset, Statement of Financial Position [Extensible List]	Property, equipment and fixtures, net	Property, equipment and fixtures, net
Future lease payment obligations that have not yet commenced but have been executed	$ 31,027
Present value of lease liabilities	$ 287,072
Number of real estate partnerships with company ownership interests | real_estate_partnership	4
Number of partnerships to which rent was paid for leased stores | real_estate_partnership	2
Rent paid to related partnership	$ 1,568	$ 1,556
Rent paid to Wakefern under sublease agreement	413	959
Lease termination expense	$ 9,500	9,800
Minimum
Lessee, Lease, Description [Line Items]
Initial lease terms	20 years
Maximum
Lessee, Lease, Description [Line Items]
Initial lease terms	30 years
Variable Interest Entity, Not Primary Beneficiary
Lessee, Lease, Description [Line Items]
Number of variable interest entity real estate partnerships | real_estate_partnership	1
Number of properties owned by VIE partnership | property	1
Percentage of profits and losses entitled to Company	33.00%
Officer
Lessee, Lease, Description [Line Items]
Officer ownership percentage in leasing property realty firm	30.00%
Lease expense	$ 735	$ 735
Affiliated Entity | Supermarket Leased From Realty Firm Which Company Officers Partially Own
Lessee, Lease, Description [Line Items]
Present value of lease liabilities	1,851
Affiliated Entity | Stores Leased From Real Estate Partnerships Which Company Has Ownership Interest In
Lessee, Lease, Description [Line Items]
Present value of lease liabilities	$ 15,996