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.util.Scanner;
import java.lang.Math;

class Main{

    public static void main(String[] args){

        Scanner scanner = new Scanner(System.in);
        long n = scanner.nextLong();
        long a = scanner.nextLong();
        long b = scanner.nextLong();
        scanner.close();

        long count = 0;
        long blue = 0;
        
        for(long i = 0; i<Math.pow(10,100); i++){
            count += a;
            if(count<=n){
                blue += a;
            }else{
                for(long j=0; j<a; j++){
                    blue += 1;
                    count = count+1-a;
                    if(count == n){
                        System.out.println(blue);
                        return;
                    }
                }
            }
            count += b;
            if(count>n){
                System.out.println(blue);
                return;
            }
        }
    }
}