Stones - Algorithm

You have stones to distribute between two piles with different weights. Each stone adds $a$ to pile 1 or $b$ to pile 2.

$1.$ Try all possible distributions: give $i$ stones to pile 1 (0 to n).

$2.$ The remaining $n - i$ go to pile 2.

$3.$ Calculate pile 1 weight: $i \times a$. Calculate pile 2 weight: $(n-i) \times b$.

$4.$ Count this as a valid outcome. Store all unique (weight1, weight2) pairs.

$5.$ The answer is how many unique pairs exist. Use a set to avoid counting duplicates.