CF1146D.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 $m$.

一只青蛙初始位于数轴上的位置 $0$。该青蛙有两个正整数 $a$ 和 $b$。从位置 $k$ 出发，它可跳至位置 $k+a$ 或 $k-b$。

定义 $f(x)$ 为：当青蛙的跳跃始终不超出区间 $[0, x]$（即不允许落在该区间外的整数上）时，它所能到达的不同整数的个数。注意，青蛙无需在一次行程中访问所有这些整数；只要存在某种方式（从 $0$ 出发）使其能够到达某个整数，该整数即被计入。

给定一个整数 $m$，求 $\sum_{i=0}^{m} f(i)$。即，求所有 $f(i)$（其中 $i$ 从 $0$ 到 $m$）的和。

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

第一行包含三个整数 $m, a, b$（$1 \leq m \leq 10^9,\ 1 \leq a,b \leq 10^5$）。

Print a single integer, the desired sum.

输出一个整数，即所求的和。

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.

在第一个例子中，我们需要计算 $f(0)+f(1)+\ldots+f(7)$。我们有 $f(0) = 1, f(1) = 1, f(2) = 1, f(3) = 1, f(4) = 1, f(5) = 3, f(6) = 3, f(7) = 8$。这些值的和为 $19$。

在第二个例子中，我们有 $f(i) = i+1$，因此需要计算 $\sum_{i=0}^{10^9} i+1$。

在第三个例子中，青蛙在任何情况下都无法进行跳跃。