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;

namespace BlueBalls
{     
    class Program
    {
        static void Main(string[] args)
        {

            long N = 0;
            long A = 0;
            long B = 0;

            Input Input = new Input();
            string input = "";

            Input.readInput(out input);
            Input.convertInput(input, out N, out A, out B);
                                   
            long remainder = Math.Min(N % (A + B), A);
            long div = N / (A + B);

            A = div * A + remainder;
            Console.WriteLine(A);
        }
    }

    class Input
    {

        public void readInput(out string input)
        {
            input = Console.ReadLine();
        }

        public void convertInput(string input, out long N, out long A, out long B)
        {
            string[] valueArray = input.Split(' ');

            N = Convert.ToInt32(valueArray[0]);
            A = Convert.ToInt32(valueArray[1]);
            B = Convert.ToInt32(valueArray[2]);
        }
    }
}