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
list($count, $blue, $red) = explode(' ', trim(fgets(STDIN)));

// 青が0の場合は計算の必要なし
if ((int)$blue === 0) {
    echo 0;
    return;
}

$roop_count = floor((int)$count / ((int)$blue + (int)$red));
$remainder = (int)$count % ((int)$blue + (int)$red);

if ((int)$blue >= $remainder) {
    echo (int)$blue * (int)$roop_count + $remainder;
} else {
    echo (int)$blue * ((int)$roop_count + 1);
}