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: Time Limit Exceeded)

<?php

fscanf(STDIN,"%d %d %d",$n,$a,$b);

$blue=0;
$red =0;

if($a == 0){
	echo 0;
}else{
  while(true){
    if($n-$a>0){
      $blue +=$a;
      $n -= $a;
    }elseif($n ==0){
      break;
    }else{
      $blue += $n % $a;
      $n =0;
    }
     if($n-$b>0){
      $red +=$b;
      $n -= $b;
    }elseif($n ==0){
       break;
     }else{
      $red += $n % $b;
      $n =0;
    }
  }
  echo $blue;
}