SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES - Additional Information (Details) shares in Thousands, $ in Thousands	12 Months Ended
	Jul. 26, 2025 USD ($) class store segment shares	Jul. 27, 2024 USD ($) shares	Jul. 29, 2023 USD ($)
Business Combination [Line Items]
Number of stores acquired | store	34
Depreciation	$ 2,256	$ 2,012
Fiscal year period	364 days	364 days
Number of operating segments | segment	1
Credit and debit card receivables	$ 12,493	$ 11,938
Percentage of LIFO inventory	64.00%
LIFO reserve inventory	$ 22,382	21,789
Operating lease assets	252,291	259,764
Present value of lease liabilities	262,801
Adjustment to retained earnings from adoption of ASU 2016-02	491,964	447,559	$ 410,166
Financing obligations	(19,280)
Advertising expense	11,582	12,174
Impairment of assets	1,462	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%
Restricted Stock Units (RSUs)
Business Combination [Line Items]
Class A shares excluded from computation of earnings per share (in shares) | shares	427	456
Buildings
Business Combination [Line Items]
Useful life	30 years
Store fixtures and equipment | Minimum
Business Combination [Line Items]
Useful life	5 years
Store fixtures and equipment | Maximum
Business Combination [Line Items]
Useful life	7 years
Vehicles
Business Combination [Line Items]
Useful life	3 years
Wakefern
Business Combination [Line Items]
Demand deposits invested at related party Wakefern	$ 92,003	$ 97,126
Gourmet Garage Specialty Markets
Business Combination [Line Items]
Number of stores acquired | store	3