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)

function Main(input) {
    input = input.split(" ");
    var n = parseInt(input[0], 10);
    var b = parseInt(input[1], 10);
    var r = parseInt(input[2], 10);
    if (n === 0 || b === 0 || r === 0) {
        console.log(0);
    } else {
        var k = n / (b + r);
        if (k == 1 || k < 1) {
            console.log(b)
        } else {
            var nk = n - (b + r) * Math.floor(k);
            if (nk >= b) {
                console.log(b * Math.floor(k) + b);
            }else { 
                console.log(b * Math.floor(k) + nk);
            }
        }
    }
}

Main(require("fs").readFileSync("/dev/stdin", "utf8"));