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.Generic;
using System.Diagnostics;
using System.Diagnostics.Contracts;
using System.Linq;

namespace at_coder
{
#if TEST
    [TestClass]
#endif
    public class Test_158_b
    {

#if TEST
        public static void Test_Main()
#else
        public static void Main()
#endif
        {
            long N, A, B;

            ReadLong(out N, out A, out B);

            long ans = N / (A + B) * A;
            long mod = Math.Min(N % (A + B), A);

            ans += mod;

            Write($"{ans}");
        }

        private static void ReadLong(out long a, out long b, out long c)
        {
            var ar = ReadLongArray();
            a = ar[0];
            b = ar[1];
            c = ar[2];
        }

        private static long[] ReadLongArray()
        {
            string[] ss = Console.ReadLine().Split(new char[] { ' ' }, StringSplitOptions.RemoveEmptyEntries);
            long[] ar = new long[ss.Length];
            for (int i = 0; i < ss.Length; i++)
            {
                ar[i] = long.Parse(ss[i]);
            }
            return ar;
        }

        private static void Write(string s)
        {
            Console.WriteLine(s);
        }

#if !TEST
    }
}
#endif