BASIS OF PRESENTATION and ACCOUNTING POLICIES - Disaggregated Revenues (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Jan. 27, 2024	Jan. 28, 2023	Jan. 27, 2024	Jan. 28, 2023
Revenue from External Customer [Line Items]
Sales	$ 575,579	$ 563,866	$ 1,111,933	$ 1,083,555
Percentage of total sales	100.00%	100.00%	100.00%	100.00%
Center Store
Revenue from External Customer [Line Items]
Sales	$ 350,573	$ 343,818	$ 671,497	$ 655,642
Percentage of total sales	60.90%	61.00%	60.50%	60.60%
Fresh
Revenue from External Customer [Line Items]
Sales	$ 202,610	$ 200,503	$ 396,130	$ 389,511
Percentage of total sales	35.20%	35.60%	35.60%	35.90%
Pharmacy
Revenue from External Customer [Line Items]
Sales	$ 20,337	$ 17,621	$ 40,548	$ 34,790
Percentage of total sales	3.50%	3.10%	3.60%	3.20%
Other
Revenue from External Customer [Line Items]
Sales	$ 2,059	$ 1,924	$ 3,758	$ 3,612
Percentage of total sales	0.40%	0.30%	0.30%	0.30%