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: Wrong Answer)

<?php

list($n, $blue, $red) = explode(' ', trim(fgets(STDIN)));

if ($blue == 0) {
  echo 0;
} elseif ($n <= $blue) {
  echo $n;
} elseif ($n > $blue && $n <= $blue + $red) {
  echo $blue;
} else {
  $n1 = floor($n / ($blue + $red));
  $n2 = $n % ($blue + $red);

  if ($n2 <= $blue) {
    echo $n2 + $blue * $n1;
  } elseif ($n2 > $blue && $n2 <= $blue + $red) {
    echo $blue + $blue * $n1;
  }
}