A12523. Frog Jumping

A frog is initially at position $0$ on the number line. The frog has two positive integers $a$ and $b$ . From a position $k$ , it can either jump to position $k+a$ or $k-b$ .

Let $f(x)$ be the number of distinct integers the frog can reach if it never jumps on an integer outside the interval $[0, x]$ . The frog doesn't need to visit all these integers in one trip, that is, an integer is counted if the frog can somehow reach it if it starts from $0$ .

Given an integer $m$ , find $\sum_{i=0}^{m} f(i)$ . That is, find the sum of all $f(i)$ for $i$ from $0$ to $m$ .

The first line contains three integers $m, a, b$ ( $1 \leq m \leq 10^9, 1 \leq a,b \leq 10^5$ ).

Print a single integer, the desired sum.

In the first example, we must find $f(0)+f(1)+\ldots+f(7)$ . We have $f(0) = 1, f(1) = 1, f(2) = 1, f(3) = 1, f(4) = 1, f(5) = 3, f(6) = 3, f(7) = 8$ . The sum of these values is $19$ .

In the second example, we have $f(i) = i+1$ , so we want to find $\sum_{i=0}^{10^9} i+1$ .

In the third example, the frog can't make any jumps in any case.