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# (.NET Core 3.1.201) (judge verdict: Time Limit Exceeded)

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

namespace Atc_0024
{
    class Program
    {
        static void Main(string[] args)
        {
            var rStr = Console.ReadLine();

            long N = long.Parse(rStr.Split(' ')[0]);
            long A = long.Parse(rStr.Split(' ')[1]);
            long B = long.Parse(rStr.Split(' ')[2]);

            if (A == 0)
            {
                Console.WriteLine(0);
                return;
            }

            long result = 0;
            long index = 0;
            double Maxi = Math.Pow(10, 100);

            while (index <= Maxi)
            {
                index++;

                if (A <= N)
                {
                    result += A;

                    N -= A;
                }
                else
                {
                    result += N;
                    break;
                }

                N -= B;

                if (N <= 0)
                {
                    break;
                }
            }

            Console.WriteLine(result);

        }
    }
}