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.util.Scanner;
import java.math.BigInteger;
class Main {
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    BigInteger n = sc.nextBigInteger(); 
    BigInteger b = sc.nextBigInteger(); 
    BigInteger r = sc.nextBigInteger();
    sc.close();
    if(b.equals(new BigInteger("0"))) {
      System.out.println("0");
    } else {
      BigInteger x = b.multiply(n.divide(n.divide(b.add(r))));
      BigInteger y = n.mod(b.add(r));
      BigInteger z = y.subtract(r);
      System.out.println(x.add(z));
    }
  }
}