Performant way to limit selected rows but make sure the sum of the rows is large enough

Question

Here's a simplified version of the problem. You have a marketplace where users can publish how many items they have for sale and the price. You would like to buy 1 000 000 items, and you want to purchase the cheapest listings first.

Example of getting all rows:

SELECT id, price, count FROM for_sale ORDER BY price ASC

In a worst-case scenario, you might need to fetch 1 000 000 rows if each user is selling one item each, but usually, users would publish more than a single item.

Is there a performant way to get only the rows needed to fulfil the purchase? E.g., for each row, a counter named total_items is incremented with count, and when total_items covers the wanted purchase amount, no more rows are returned.

Using LIMIT reduces the number of rows returned, but I can't be sure how many rows are needed as it depends on each row's count.

What I've tried so far

SET @total := 0;
SELECT id, count, price, @total := @total + count AS total
FROM for_sale
WHERE @total < 1000000 ORDER BY `price` ASC;

This query somewhat works, but the user variable check seems to be done client-side resulting in up to seven additional rows where the total is over 1 000 000. The performance is also terrible compared to just a LIMIT(more than 300x execution time).

I've also tried to use a window function, but I'm not sure if that's possible without reading the whole table.

Is there a way to only select rows that covers the purchase amount instead of every row? I've searched a lot, and the only examples I've found is user variable ones that suffer from performance issues.