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";
main(
  require("fs")
    .readFileSync("/dev/stdin", "UTF-8")
    .trim()
    .split("\n")
);
function main(input) {
  input = input[0].split(" ").map(Number);
  const N = input[0];
  const A = input[1];
  const B = input[2];
  let result;

  if (N < A + B) {
    if (N > A) result = N;
    else result = A;
  } else {
    result = Math.floor(N / (A + B)) * A;
    if (Math.floor(N % (A + B)) > A) result += A;
    else result += Math.floor(N % (A + B));
  }

  console.log(result);
}