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

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main {
    public static void main(String[] args) throws IOException {
        MyReader reader = new MyReader();
        int[] nab = reader.readInts(" ");
        int n = nab[0];
        int a = nab[1];
        int b = nab[2];
        System.out.println(problem158b(n, a, b));
    }

    private static int problem158b(int n, int a, int b) {
        return a * (n / (a + b)) + (Math.min(a, (n % (a + b))));
    }

    private static class MyReader {
        private final BufferedReader br;
        private MyReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        private String readString() throws IOException {
            return br.readLine();
        }

        private int readInt() throws IOException {
            return Integer.parseInt(readString());
        }

        private String[] readStrings(String regex) throws IOException {
            return readString().split(regex);
        }

        private int[] readInts(String regex) throws IOException {
            String[] strings = readStrings(regex);
            int[] ints = new int[strings.length];
            for (int i = 0; i < ints.length; i++) {
                ints[i] = Integer.parseInt(strings[i]);
            }
            return ints;
        }
    }
}