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 PHP7 (7.0.15) (judge verdict: Accepted)

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

  for ($i = 0; $i < 3; $i++) {
    $inp[$i] = intval($inp[$i]);
  }
  if ($inp[0] === 0) {
    return print("0\n");
  }

  $sum = $inp[1] + $inp[2];
  $quot = intval($inp[0] / $sum) * $inp[1];
  $sur = $inp[0] % $sum;

  if ($inp[1] < $sur) {
    $quot += $inp[1];
  } else {
    $quot += $sur;
  }

  printf("%s\n", $quot);

?>