Frog Jumping

2000ms

262144K

Description:

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 $$$m$$$.

Input:

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

Output:

Print a single integer, the desired sum.

Sample Input:

7 5 3

Sample Output:

Sample Input:

1000000000 1 2019

Sample Output:

500000001500000001

Sample Input:

100 100000 1

Sample Output:

Sample Input:

6 4 5

Sample Output:

Note:

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.

Informação

Provedor Codeforces

Código CF1146D