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: Wrong Answer)

import java.math.BigDecimal;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);

		double N = sc.nextDouble();
		double A = sc.nextDouble();
		double B = sc.nextDouble();

		double ballCount = 0;
		double blueBallCount = 0;

		double i = 1;
		while (true) {
			if (i % 2 != 0) {
				ballCount += A;
				blueBallCount += A;
			} else {
				ballCount += B;
			}

			if (ballCount >= N) {
				if (i % 2 != 0) {
					blueBallCount = blueBallCount - (ballCount - N);
				}
				break;
			}
			i++;
		}

		BigDecimal result = new BigDecimal(blueBallCount);
		System.out.println(result);

		sc.close();
	}
}