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', $n, $a, $b);

if ($a <= 0) {
    echo '0' . PHP_EOL;
    exit;
}

$blueAry = array_fill(0, $a, 0);
$redAry = array_fill(0, $b, 1);
$ary = array_merge($blueAry, $redAry);

$column = [];
while(count($column) <= $n) {
    $column = array_merge($column, $ary);
}

echo count(array_keys(array_slice($column, 0, $n), 0));

echo PHP_EOL;
?>