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: Runtime Error)

using System;
class AtCoder
{
    static void Main(string[] args)
    {
      	var str = Console.ReadLine().Split(' ');
      	var n = int.Parse(str[0]);
      	var a = int.Parse(str[1]);
      	var b = int.Parse(str[2]);
       
        var blue = true;
      	var cnt = 0;
      	var bc = 0;
        for(var i = 0 ; i < n ; i ++ ){
          if( blue ){            
            if( bc++ == a ){
              i--;
              bc = 0;
              blue = false;
            }
            else{
              cnt++;
            }
          }
               else{
                 if( bc++ == b ){
                   i--;
                   bc = 0;
                   blue = true;
                 }
               }
        }
      
      Console.WriteLine(cnt.ToString());
    }
}