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.*;

class Main{
    public static void main(String[] args)throws IOException{
      try(BufferedReader br = new BufferedReader(new InputStreamReader(System.in))){
        //input
        String[] input = br.readLine().split(" ");
        
        int N = Integer.parseInt(input[0]);
        int A = Integer.parseInt(input[1]); //blue
        int B = Integer.parseInt(input[2]); //red

        //for output
        int result = 0;

        //for algorithm
        int num = 0;
        int count = 0;

        while(true){
          if(count == 0){
            num += A;
            count++;
            if(num > N){
              result = N;
              break;
            }else{
              result += num;
            }
          }else{
            if((count % 2) != 0){
              num += B;
              count++;
              if(num > N){
                break;
              }else{
                continue;
              }
            }else if((count % 2) == 0){
              num += A;
              count++;
              if(num > N){
                result += A - (num - N);
                break;
              }else{
                result += A;
              }
            }
          }
        }
        
        System.out.println(result);
    
      }
    }
}