I found that "the" is the right article, but could not find why here is impossible to use "a". Saorsa, thank you a lot. All are fully explained. Sometimes it's a little bit complicated to understand these features for non-foreigners.

This is grammatically correct, but a bit odd. The kind of context where you would say it this way would be a bit unusual, it sounds like you’re telling a story that happened years ago. Most likely, you want to say “the supermarket”. There is a rule about when to use “the” and “a”, that goes something like the first time you mention something it’s “a” (when it’s new info and the listener doesn’t know about it yet), then after that it’s “the” (when the listener knows what you’re talking about).. but, it’s not so simple.. sometimes things are “the” even if they are new information.. sometimes you can use “the” to shift the focus.. sometimes.. Say you came back from a holiday in Portugal, you might say: I went swimming at the beach every day as the listener I would be expecting you to continue talking about other activities you did - the focus is on the swimming. or you could also say: I went swimming at a beach every day This sounds like you had to go out of your way to find the beach, and I’m kinda expecting you to tell me about the beach - the focus is more on the beach. I think because supermarkets are part of the background radiation of living in the early 21st century, we often just call it “the supermarket”, even if it’s in a new city and you’ve never been to that particular one before. Another example, the other day a friend commented on a cup that I had, and I said “yeah, I found it on the side of the road”. Because it’s not important which particular road I found it on, I can just call it “the road”, as if all roads really are just one big piece of tarmac - much like the way we talk about “the ocean” as one big soup, and it doesn’t matter if you mean the Pacific or the Arctic. But then again, you couldn’t say “I sat in the café to get free wifi” without introducing the coffee shop first, you’d have to use “a café”. I guess cafés are more distinctive than beaches, oceans and supermarkets (perhaps?)

That's correct