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: Time Limit Exceeded)

import java.io.PrintWriter;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {

		try (Scanner scan = new Scanner(System.in); PrintWriter out = new PrintWriter(System.out);) {
			long n = Long.parseLong(scan.next());
			long a = Long.parseLong(scan.next());
			long b = Long.parseLong(scan.next());

			long ret = 0;

			while (true) {

				n -= a;
				ret += a;

				if (n < 0) {
					ret += n;
					break;
				}

				n -= b;
				if (n < 0) {
					break;
				}
			}

			out.println(ret);
			out.flush();
		}
	}
}