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;
using System.Linq;

namespace ConsoleApp1
{
    class Program
    {
        static void Main(string[] args)
        {
            var line1 = Console.ReadLine().Split(' ');
            var n = int.Parse(line1[0]);
            var a = int.Parse(line1[1]); //blue
            var b = int.Parse(line1[2]); //red

            var retu = new List<char>();

            while (retu.Count < n)
            {
                for (var j = 0; j < a; j++)
                {
                    retu.Add('A');
                }
                for (var k = 0; k < b; k++)
                {
                    retu.Add('B');
                }
            }

            var ans = 0;

            for (var l = 0; n > l; l++)
            {
                if (retu[l] == 'A') ans++;
            }
            Console.WriteLine(ans);
        }
    }
}