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

namespace _158_A
{
    class Program
    {
        static void Main(string[] args)
        {
            string input = ReadLine();
            string[] array = input.Split(' ');
            ulong[] n = new ulong[array.Length];
            for (int i = 0; i < array.Length; i++)
            {
                n[i] = ulong.Parse(array[i]);
            }
            ulong sum = n[1] + n[2];
            ulong result1 = n[0] / sum;
            ulong result2 = n[0] % sum;
            ulong result3 = 0;
            if (result2 > n[1])
            {
                result3 = result1 * n[1] + n[1];
            }
            else {
                result3 = result1 * n[1] + result2;
            }
            WriteLine("{0}", result3);
            ReadKey();
        }
    }
}