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.util.Scanner;

public class Main {
    public static void main(String[] args) throws Exception {
        long checkNum;
        long blueBall;
        long redBall;

        Scanner scanner = new Scanner(System.in);
        String inputData = scanner.nextLine();
        scanner.close();

        String[] editedInputData = inputData.split(" ");
        checkNum = Integer.parseInt(editedInputData[0]);
        blueBall = Integer.parseInt(editedInputData[1]);
        redBall = Integer.parseInt(editedInputData[2]);

        long blueAndRed = blueBall + redBall;
        long countBall = checkNum % blueAndRed;
        long innerBlueAndRedBallSet = checkNum / blueAndRed;
        
        long totalBlueBall = innerBlueAndRedBallSet * blueBall;

        if (countBall <= blueBall) {
            totalBlueBall += countBall;
        } else {
            totalBlueBall += blueBall;
        }

        System.out.println(totalBlueBall);

    }
}