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)

using System;
using System.Collections.Generic;

namespace CodingForces
{
    static class Program
    {
        static void Main(string[] args)
        {
            int[] nbrs = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
            int num = 0;
            int numBlues = 0;
            List<string> row = new List<string>();

            while (num < nbrs[0])
            {
                for (int i = 0; i < nbrs[1]; i++)
                {
                    if (num < nbrs[0])
                    {
                        row.Add("b");
                        num++;
                        numBlues++;
                    }
                    else
                    {
                        break;
                    }
                }
                for (int j = 0; j < nbrs[2]; j++)
                {
                    if (num < nbrs[0])
                    {
                        row.Add("r");
                        num++;
                    }
                    else
                    {
                        break;
                    }
                }
            }
            Console.WriteLine(numBlues);
            //Console.ReadKey();
        }
    }
}