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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

"use strict";

const main = arg => {
    // 標準入力の不要な空白と改行を削除し、配列に格納する
    const input = arg.trim().split(" ");
    const N = parseInt(input[0], 10);
    const blue =parseInt(input[1], 10);
    const red = parseInt(input[2], 10);
    
    const sum = blue + red;
    const times = Math.floor((N / sum), 10);
    const amari = N % sum;
    
    if (times === 0) {
        (N > blue)? console.log(blue) : console.log(N);
    }else{
        if (amari > blue) {
            console.log((blue * times) + blue)
        } else {
            console.log((blue * times) + amari); 
        }
    }
}

main(require('fs').readFileSync('/dev/stdin', 'utf8'));