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: Time Limit Exceeded)

<?php
fscanf(STDIN, '%d %d %d', $cnt, $blue, $red);
if ($blue === 0) {
    echo 0;
    echo "\n";
    exit;
}
if ($red === 0) {
    echo $cnt;
    echo "\n";
    exit;
}
$ans = 0;
$blueFlag = true;
$tmp = 0;
for ($i=1; $i <= $cnt; $i++) { 
    if ($blueFlag) {
        $ans++;
    }
    $tmp++;
    if ($blueFlag && $tmp % $blue === 0 || !$blueFlag && $tmp % $red === 0) {
        $blueFlag = !$blueFlag;
        $tmp = 0;
    }
}
echo $ans;
echo "\n";