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;
using System.Text;
using System.Threading.Tasks;
 
namespace Atcoder
{
    class Program
    {
        static void Main(string[] args)
        {
          string[] input_line = Console.ReadLine().Trim().Split(' ');
          int a = int.Parse(input_line[0]);
          int b = int.Parse(input_line[1]);
          int c = int.Parse(input_line[2]);
          
          int ballNum = 0;
          do
          {
            if(a>0)
            {
              a -= b;
              if(a <= 0)
              {
                ballNum += a;
              }
              ballNum += b;
            }
            if(a > 0)
            {
              a -= c;
            }
          }while(a > 0);
          
          Console.WriteLine(ballNum);
        }
    }
}