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)

public class Main {

    static java.util.Scanner scan = new java.util.Scanner(System.in);

    public static void main(String[] args) {
        int[] line = getLineInts();
        char[] var = new char[line[0]];
        int i =0;
        boolean f = true;
        int a = 0;
        int b = 0;
        if(line[1] == 0){
            puts("0");
            return;
        }else if(line[2] == 0){
            puts(String.valueOf(line[2]));
            return;
        }
        while (i<var.length){
            if(f){
                var[i] = 'a';
                i++;
                a++;
                if(a % line[1] == 0){
                    f = false;
                    a = 0;
                }
            }else{
                var[i] = 'b';
                i++;
                b++;
                if(b % line[2] == 0){
                    f = true;
                    b = 0;
                }
            }
        }
        int c = 0;
        for(i=0;i<var.length;i++){
            if(var[i] == 'a'){
                c++;
            }
        }
        puts(String.valueOf(c));
    }



    public static void puts(String mes){
        System.out.println(mes);
    }

    public static int[] getLineInts(){
        return java.util.stream.Stream.of(getLine()).mapToInt(Integer::parseInt).toArray();
    }

    public static String[] getLine(){
        return scan.nextLine().split(" ");
    }
}