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 PHP (5.6.30) (judge verdict: Wrong Answer)

<?php
  $input = explode(' ', fgets(STDIN));

  $N = (int)$input[0];
  $A = (int)$input[1];
  $B = (int)$input[2];

  $AB = $A + $B;

  if($A === 0) return print("0\n");

  $ans = floor($N / $AB) * $A;

  $bb = (int)$N % $AB;

  if($A < $bb) {
    $ans += $A;
  } else {
    $ans += $bb;
  }

  printf("%s\n", $ans);
?>