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 Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.io.*;
import java.util.*;
import java.util.ArrayList;
 
class Main
{
  public static void main (String[] arg)
  {
    Scanner scan = new Scanner(System.in);
    
    int N = Integer.parseInt(scan.next()); //整数    
    int A = Integer.parseInt(scan.next()); //整数    蒼
    int B = Integer.parseInt(scan.next()); //整数　　赤
    
    if(A == 0 && B == 0){
      System.out.println(0);
    }
    
    else{
      
      ArrayList<String> array = new ArrayList<>();
      
      int dekai = (int)Math.pow(10, 100);
      
      for(int i = 0;i < dekai;i++){
      
        for(int j = 0;j < A;j++){ 
          array.add("b");
        }
        for(int j = 0;j < B;j++){ 
          array.add("r");
        }
        if(array.size() > N){
          break;
        }
      }
      int count_b = 0; //青の数
      for(int i = 0;i < N;i++){ 
          if(array.get(i) == "b"){
            count_b++;
        }
      }
      System.out.println(count_b);
      }
  }
}