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: Wrong Answer)

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

public class Hello
{
    public static void Main()
    {
        hoge();
        System.Console.ReadLine();
    }

    public static void hoge()
    {
        var vars = System.Console.ReadLine().Split(' ').Select(x => ulong.Parse(x)).ToArray();
        ulong n = vars[0];
        ulong a = vars[1];
        ulong b = vars[2];

        if(a == 0)
        {
            System.Console.WriteLine(0);
            return;
        }

        ulong ans = 0;
        for(ulong count = 0; ; count +=  a + b) {
            ulong tmp = a;

            if (count + a > n)
            {
                ans += n - count;
                break;
            }
            ans += tmp;
        }

        System.Console.WriteLine(ans);


    }

}