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;
using System.Linq;

namespace Main
{
    class Program
    {
        static void Main(string[] args)
        {
            //ここから
            //string[] str = Console.ReadLine().Split(' ');
            //int n = int.Parse(Console.ReadLine());

            string[] str = Console.ReadLine().Split(' ');
            long n = long.Parse(str[0]);
            long a = long.Parse(str[1]);
            long b = long.Parse(str[2]);

            long ans = 0;

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

            while(true)
            {
                if (n > a)
                {
                    n -= a;
                    ans += a;
                }
                else
                {
                    ans += n;
                    break;
                }

                if (n > b)
                {
                    n -= b;
                }
                else { break; }
            }

            Console.WriteLine(ans);

            //ここまで
        }
    }
}