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;

namespace abc159B
{
    class MainClass
    {
        public static void Main(string[] args)
        {
            string S = Console.ReadLine();
            int N = S.Length;
            string[] A = new string[N];
            for(int i = 0; i < N; i++)
            {
                A[i] = S.Substring(i, 1);
            }
            int X = 0;
            for(int i = 0; i < N/2; i++)
            {
                if (A[i] != A[N - 1 - i])
                    X += 1;
            }
            for (int i = 0; i < ((N - 1) / 2) / 2; i++)
            {
                if (A[i] != A[((N - 1) / 2) - 1 - i])
                    X += 1;
            }
            for(int i = (N + 3) / 2 - 1; i < (N- ((N + 3) / 2))/2; i++)
            {
                if (A[i] != A[N - 1 - i])
                    X += 1;
            }
            if (X == 0)
                Console.WriteLine("Yes");
            else
                Console.WriteLine("No");
        }
    }
}