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: Accepted)

using System;


class Program
{
    static void Main(string[] args)
    {
        string[] input = Console.ReadLine().Split(' ');
        long N = long.Parse(input[0]);
        long A = long.Parse(input[1]);
        long B = long.Parse(input[2]);

        if(A == 0)
        {
            Console.WriteLine(0);
        }
        else if (N <= A)
        {
            Console.Write(N);
        }
        else if (N <= A + B)
        {
            Console.Write(A);
        }
        else
        {
            long x = N / (A + B);
            long y = N % (A + B);

            if(A < y)
            {
                Console.Write((A * x) + A);
            }
            else
            {
                Console.Write((A * x) + y);
            }
        }
    }
}