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
$input = file_get_contents('php://stdin');
$inarr = explode(" ", $input);

$n = intval($inarr[0]);
$a = intval($inarr[1]);
$b = intval($inarr[2]);

if($a==0){
	echo "0";
  	exit();
}

$num = (int)floor($n/($a+$b));
$fraction = $n%($a+$b);
$total = $num * $a;
if($fraction>$a){
    $total+=$a;
}
else{
    $total+=$fraction;
}

//echo $total;
printf("%s\n", $total);
?>