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: Time Limit Exceeded)

import java.util.*;
public class Main{
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    long n = sc.nextLong();
    long a = sc.nextLong();
    long b = sc.nextLong();
    long c = (long)Math.pow(10,18);
    long num = 0;
    long count = 0;

    for(long i=c ; i>0 ; i--){
      num = num + a*i;
    }
    String s = String.valueOf(num);

    for(int i=0 ; i<n ; i++){
      if(s.charAt(i)=='a'){
        count++;
      }
    }
    System.out.println(count);
  }
}