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.math.BigInteger;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);

		BigInteger N = BigInteger.valueOf(sc.nextInt());
		BigInteger blue = BigInteger.valueOf(sc.nextInt());
		BigInteger red = BigInteger.valueOf(sc.nextInt());

		BigInteger total = BigInteger.valueOf(0);
		BigInteger blueCount = BigInteger.valueOf(0);

		while(true)
		{
			total = total.add(blue);
			blueCount = blueCount.add(blue);

			if(N.compareTo(total) <= 0)
			{
				blueCount = blueCount.subtract(total.subtract(N));
				break;
			}

			total = total.add(red);

			if(N.compareTo(total) <= 0) break;

		}

		System.out.println(blueCount);

	}
}