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.IO;
using System.Linq;

namespace AtCoder {
	class Program {
		public static void Main(string[] args) {
			Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
			long[] input = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
			long n = input[0];
			long a = input[1];
			long b = input[2];
			long sum = 0;
			//for (long i = 0; i <= n / (a + b); i++) sum += a;
			if (a == 0) {
				sum = 0;
			} else {
				sum = n / (a + b) * a;
				sum += n % (a + b) < a ? n % (a + b) : a;
			}
			Console.WriteLine(sum);
			Console.Out.Flush();
		}
	}
}