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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;

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

            var retu = new List<char>();

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

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