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: Accepted)

using System;
using System.Linq;

public class AtCoder_158_B
{
    public static void Main()
    {
        long[] line1 = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
        long count = line1[0];
        long b = line1[1];
        long r = line1[2];

        if (b == 0 && r == 0)
        {
            Console.WriteLine(0);
            return;
        }

        long bCount = count / (b + r) * b;
        long amari = count % (b + r);
        bCount += (amari > b ? b : amari);

        Console.WriteLine(bCount);
    }
}