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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Atcoder
{
    class Program
    {
        static void Main(string[] args)
        {
            var arg = Console.ReadLine().Split(' ');
            var N = arg[0].ToDecimal();
            var A = arg[1].ToDecimal();
            var B = arg[2].ToDecimal();
            double count = Math.Pow(10, 18);
            decimal red = 0;
            decimal blue = 0;
            for (int i = 1; i <= count; i++)
            {
                var total = red + blue;
                var isRed = i % 2 == 0;
                if (isRed)
                {
                    if(N < total + B)
                    {
                        red += N - total;
                    }
                    else
                    {
                        red += B;
                    }
                }
                else
                {
                    if (N < total + A)
                    {
                        blue += N - total;
                    }
                    else
                    {
                        blue += A;
                    }
                }
                if (red + blue >= N)
                {
                    break;
                }
            }
            Console.WriteLine((blue.ToString()));
        }
    }

    public static class Extentions
    {
        public static int ToInt(this object obj)
        {
            return int.Parse(obj.ToString());
        }

        public static decimal ToDecimal(this object obj)
        {
            return decimal.Parse(obj.ToString());
        }
    }
}