SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES - Additional Information (Details) shares in Thousands, $ in Thousands	12 Months Ended
	Jul. 27, 2024 USD ($) store segment class shares	Jul. 29, 2023 USD ($) shares	Jul. 30, 2022 USD ($)
Business Acquisition [Line Items]
Number of stores acquired | store	34
Depreciation	$ 2,012	$ 1,709
Fiscal year period	364 days	364 days
Number of operating segments | segment	1
Credit and debit card receivables	$ 11,938	$ 11,891
Percentage of LIFO inventory	64.00%
LIFO reserve inventory	$ 21,789	21,238
Operating lease assets	259,764	274,100
Present value of lease liabilities	277,373
Adjustment to retained earnings from adoption of ASU 2016-02	447,559	410,166	$ 372,109
Financing obligations	(20,404)
Advertising expense	12,174	10,658
Impairment of assets	2,125
Indefinite-lived intangible assets	$ 13,299	$ 13,299
Number of common stock classes | class	2
Common stock cash dividends, percent Class A is entitled greater than Class B	54.00%
Class A Common Stock
Business Acquisition [Line Items]
Class A shares excluded from computation of earnings per share (in shares) | shares		88
Restricted Stock Units (RSUs)
Business Acquisition [Line Items]
Class A shares excluded from computation of earnings per share (in shares) | shares	456	503
Buildings
Business Acquisition [Line Items]
Useful life	30 years
Store fixtures and equipment | Minimum
Business Acquisition [Line Items]
Useful life	5 years
Store fixtures and equipment | Maximum
Business Acquisition [Line Items]
Useful life	7 years
Vehicles
Business Acquisition [Line Items]
Useful life	3 years
Wakefern
Business Acquisition [Line Items]
Demand deposits invested at related party Wakefern	$ 97,126	$ 122,028
Gourmet Garage Specialty Markets
Business Acquisition [Line Items]
Number of stores acquired | store	3