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;
 
public class Hello{
	public static void Main(){
      string[] s =Console.ReadLine().Split(' ');
      long N,A,B,r,m;
      N = long.Parse(s[0]);
      A = long.Parse(s[1]);
      B = long.Parse(s[2]);
      if(A==0){
        Console.WriteLine(0);
      }
      else if(A>=N){
        Console.WriteLine(N);
      }
      else if(A<N&&A+B>=N){
        Console.WriteLine(A);
      }
      else{
        m=N/(A+B);
        r=N%(A+B);
        if(r<A){
          Console.WriteLine(A*m+r);
        }
        else Console.WriteLine(A*(m+1));
      }
    }
}