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: Accepted)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Main {
    static PrintWriter out;

    public static void main(String[] args) throws IOException {
        out = new PrintWriter(new OutputStreamWriter(System.out));
        CF_Reader in = new CF_Reader();

        long n = in.longNext();
        long blue = in.longNext();
        long red = in.longNext();

        long rem = n % (blue + red);
        long totalBlue = ((n - rem) / (blue + red)) * blue;
        totalBlue += Math.min(blue, rem);
        out.println(totalBlue);

        out.close();
    }


    static class CF_Reader {
        BufferedReader br;
        StringTokenizer st;

        public CF_Reader() throws IOException {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine().trim());
            return st.nextToken();
        }

        long longNext() throws IOException {
            return Long.parseLong(next());
        }

        int intNext() throws IOException {
            return Integer.parseInt(next());
        }

        double doubleNext() throws IOException {
            return Double.parseDouble(next());
        }

        char charNext() throws IOException {
            return next().charAt(0);
        }

        String Line() throws IOException {
            return br.readLine().trim();
        }
    }
}