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

class Program 
{
static void solve_CountBalls(string input)
        {
            var inputs = input.Split(' ');
            if (inputs.Length != 3) return;

            long n = long.Parse(inputs[0]);
            double limit = Math.Pow(n, 18);

            if (1 > n && n > limit) return;

            long b = long.Parse(inputs[1]);
            long r = long.Parse(inputs[2]);

            if (b == 0 && r == 0) return;
            if ((b + r) > limit) return;

            Console.WriteLine(b);          
        }

        static void Main(string[] args)
        {
            solve_CountBalls(Console.ReadLine());
        }
}