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"
function main(arg) {
    var data = arg.trim().split("\n")[0].split(" ").map(Number)
    var N = data[0]
    var A = data[1]
    var B = data[2]
    if (A === 0) {
        console.log(0)
        return
    }
    var a = Math.round(N / (A+B))
    var _N = N - (a * (A+B))
    var b = 0
    for (var i = 1; i <= _N; i++) {
        if (i % (A + B) <= A && i % (A + B) !== 0) {
            b++
        }
    }
    var ans = (a * A) + b
    console.log(ans)

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