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.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoders {
	class Program {
		static void Main(string[] args) {
var inputArray = new string[3];
			inputArray = Console.ReadLine().Split(' ');

			// 不正な入力は処理しない
			if (inputArray.Length != 3) {
				Console.WriteLine("invalid input");
				return;
			}

			// 入力値セット
			var N = long.Parse(inputArray[0]);
			var A = long.Parse(inputArray[1]);
			var B = long.Parse(inputArray[2]);

			var shou = N / (A + B);
			var amari = N % (A + B);

			var answer = shou * A + Math.Min(A, amari);
			Console.WriteLine(answer);
		}
	}
}