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.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using Console = System.Console;

namespace Atcoder
{
    class Program
    {
        static void Main(string[] args)
        {
            var NAB = ReadLongArray();
            var div = NAB[0] / (NAB[1] + NAB[2]);
            var lastBlue = NAB[0] % (NAB[1] + NAB[2]);
            lastBlue = lastBlue >= NAB[1] ? NAB[1] : lastBlue;
            Console.WriteLine(div * NAB[1] + lastBlue);
        }
        private static readonly Func<string> Read = () => Console.ReadLine();
        private static readonly Func<string[]> ReadStringArray = () => Console.ReadLine().Split();
        private static readonly Func<int> ReadInt = () => int.Parse(Console.ReadLine());
        private static readonly Func<long> ReadLong = () => long.Parse(Console.ReadLine());
        private static readonly Func<int[]> ReadIntArray = () => Console.ReadLine().Split().Select(int.Parse).ToArray();
        private static readonly Func<long[]> ReadLongArray = () => Console.ReadLine().Split().Select(long.Parse).ToArray();
        private static readonly Action<string> Cw = str => Console.WriteLine(str);
    }
}