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;

namespace AtCoder.Problems
{
    public class ProblemB
    {
        public static void Main(string[] args)
        {
            var s = new SolveB();
            s.Solve();
        }

        public class Scanner
        {
            private string[] _s;
            private int _i;
            private readonly char[] _separators = new char[] { ' ' };

            public Scanner()
            {
                _s = new string[0];
                _i = 0;
            }

            public string Next()
            {
                if (_i < _s.Length) return _s[_i++];
                string st = Console.ReadLine();
                while (st == "") st = Console.ReadLine();
                _s = st.Split(_separators, StringSplitOptions.RemoveEmptyEntries);
                if (_s.Length == 0) return Next();
                _i = 0;
                return _s[_i++];
            }

            public int NextInt() => int.Parse(Next());
            public long NextLong() => long.Parse(Next());
            public ulong NextULong() => ulong.Parse(Next());
            public double NextDouble() => double.Parse(Next());

            public int[] GetIntArray(int n, int add = 0)
            {
                int[] array = new int[n];
                for (int i = 0; i < n; i++)
                {
                    array[i] = NextInt() + add;
                }
                return array;
            }

            public long[] GetLongArray(int n, long add = 0)
            {
                long[] array = new long[n];
                for (int i = 0; i < n; i++)
                {
                    array[i] = NextLong() + add;
                }
                return array;
            }

            public double[] GetDoubleArray(int n, double add = 0)
            {
                double[] array = new double[n];
                for (int i = 0; i < n; i++)
                {
                    array[i] = NextDouble() + add;
                }
                return array;
            }
        }
    }

    public class SolveB
    {
        public void Solve()
        {
            var cin = new ProblemB.Scanner();
            var n = cin.NextLong();
            var a = cin.NextLong();
            var b = cin.NextLong();

            var result = GetAnswer(n, a, b);
            Console.WriteLine(result);
        }

        public long GetAnswer(long n, long a, long b)
        {
            return n / (a + b) * a + Math.Min(n % (a + b), a);
        }
    }
}