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;

namespace A
{
    class Program
    {
        static void Main(string[] args)
        {
            var A = Console.ReadLine().Split(' ');
            ulong a = ulong.Parse(A[0]);
            ulong b = ulong.Parse(A[1]);
            ulong c = ulong.Parse(A[2]);
            var d = Math.Pow(10, 100);
            ulong cnt = 0;
            for (int i = 0; i < d; i++)
            {
                if (a >= b)
                {
                    cnt += b;
                    a -= b;
                }
                else
                {
                    cnt += a;
                    break;
                }
                if (a >= c)
                {
                    a -= c;
                }
                else
                {
                    break;
                }
            }
            Console.WriteLine(cnt);
        }
    }
}