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;

public class Program
{
    public static void Main(string[] args)
    {
        var vals = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
        if (vals[0] > vals[1] + vals[2])
        {
            var tmp = vals[0] % (vals[1] + vals[2]);
            var val = new List<string>();
            for (int i = 0; i < vals[1]; i++)
            {
                val.Add("b");
            }
            for (int i = 0; i < vals[2]; i++)
            {
                val.Add("r");
            }
            var tmp2 = Math.Floor((double)vals[0] / (vals[1] + vals[2]));
            Console.WriteLine(val.GetRange(0, tmp).Where(x => x == "b").Count() + vals[1] * (int)tmp2);
        }
        else
        {
            var val = new List<string>();
            for (int i = 0; i < vals[1]; i++)
            {
                val.Add("b");
            }
            for (int i = 0; i < vals[2]; i++)
            {
                val.Add("r");
            }
            Console.WriteLine(val.GetRange(0, vals[0]).Where(x => x == "b").Count());
        }
    }
}