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 C# (Mono 4.6.2.0) (judge verdict: Runtime Error)

public class Hello {
    
    public static int CountChar(string s,char c)
    {
        return s.Length - s.Replace(c.ToString(),"").Length;
    }
    
    public static void Main() {
        var line = System.Console.ReadLine();
        string[] array = line.Split(' ');
        
        int n = int.Parse(array[0]);
        int a = int.Parse(array[1]);
        int b = int.Parse(array[2]);
        
        
        string add_blue = new string('b',a);
        string add_red = new string('r',b);
        
        string str = "";
        string add = add_blue + add_red;
        while(str.Length < n)
        {
            str += add;
        }
        
        str = str.Substring(0,n);
        
        System.Console.WriteLine(CountChar(str,'b'));

    }
}