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;

namespace ConsoleApp2
{
    class Program
    {
        static void Main()
        {
            var info = Console.ReadLine().Split(' ');
            var range = Int64.Parse(info[0]);
            var blue = Int64.Parse(info[1]);
            var red = Int64.Parse(info[2]);
            if (blue + red == 0)
            {
                Console.WriteLine(0);
            }
            else
            {
                Int64 time = range / (blue + red);
                var ans = time * blue;
                var rem = range % (blue + red);
                if (rem >= blue)
                {
                    ans += blue;
                }
                else
                {
                    ans += rem;
                }
                Console.WriteLine(ans);
            }
            //Console.ReadKey();
        }
    }
}