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 Perl (v5.18.2) (judge verdict: Time Limit Exceeded)

use strict;
use warnings;

my ($n, $a, $b);
{
  my $in = <STDIN>;
  ($n, $a, $b) = split(" ", $in);
}
if ($a==0) {
  print "0\n";
  exit
}
my $ans = 0;
while ($n>0) {
  $ans += $a;
  $n -= $a;
  if ($n<0) {
    $ans += $n;
  } else {
    $n -= $b;
  }
}
print "$ans\n";