Problem:
Score : 200 points

Problem Statement

Takahashi has many red balls and blue balls. Now, he will place them in a row.

Initially, there is no ball placed.

Takahashi, who is very patient, will do the following operation 10^{100} times:

Place A blue balls at the end of the row of balls already placed. Then, place B red balls at the end of the row.

How many blue balls will be there among the first N balls in the row of balls made this way?

Constraints

1 \leq N \leq 10^{18}

A, B \geq 0

0 < A + B \leq 10^{18}

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N A B

Output

Print the number of blue balls that will be there among the first N balls in the row of balls.

Sample Input 1

8 3 4

Sample Output 1

4

Let b denote a blue ball, and r denote a red ball. The first eight balls in the row will be bbbrrrrb, among which there are four blue balls.

Sample Input 2

8 0 4

Sample Output 2

0

He placed only red balls from the beginning.

Sample Input 3

6 2 4

Sample Output 3

2

Among bbrrrr, there are two blue balls.

Solution in C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>

int main (){
  int n, a, b, bolasContadas=0,totalBolasAzuis=0;
  int bolaDaVez = 0; // 0 => Azul | 1 => Vermelho

  scanf("%d", &n);
  scanf("%d", &a);
  scanf("%d", &b);

  if (a==0){
    printf("0\n");
    return 0;
  }

  for (int i=1; i <= n; i++){
    if(bolaDaVez == 0 && bolasContadas == a) {
      bolaDaVez = 1;
      bolasContadas = 0;
    } else if(bolaDaVez == 1 && bolasContadas == b) {
      bolaDaVez = 0;
      bolasContadas = 0;
    }

    if (bolaDaVez == 0){
      totalBolasAzuis++;
    }

    bolasContadas++;
  }

  printf("%d\n", totalBolasAzuis);

  return 0;
}