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 Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.util.*;
import java.lang.*;
import java.io.*;


public class Main {
    public static void main(String[] args) throws java.lang.Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader((System.in)));
        StringTokenizer s = new StringTokenizer(br.readLine());
        int n = Integer.parseInt(s.nextToken());
        int blue = Integer.parseInt(s.nextToken());
        int red = Integer.parseInt(s.nextToken());
        int totalBlue = blue;
        int totalRed = red;
        while (n > totalBlue + totalRed) {
            if (blue + totalBlue + totalRed > n)
                totalBlue += (n - (totalBlue + totalRed));
            else
                totalBlue += blue;
            if (red + totalBlue + totalRed > n)
                totalRed += (n - (totalBlue + totalRed));
            else
                totalRed += red;
        }
        if (totalBlue + totalRed == n) System.out.println(totalBlue);
        else if (n >= totalBlue) System.out.println(totalBlue);
        else System.out.println(n);
    }
}