Problem:
Score : 300 points

Problem Statement

You are given an integer N.

Find a triple of positive integers h, n and w such that 4/N = 1/h + 1/n + 1/w.

If there are multiple solutions, any of them will be accepted.

Constraints

It is guaranteed that, for the given integer N, there exists a solution such that h,n,w \leq 3500.

Inputs

Input is given from Standard Input in the following format:

N

Outputs

Print a triple of positive integers h, n and w that satisfies the condition, in the following format:

h n w

Sample Input 1

2

Sample Output 1

1 2 2

4/2 = 1/1 + 1/2 + 1/2.

Sample Input 2

3485

Sample Output 2

872 1012974 1539173474040

It is allowed to use an integer exceeding 3500 in a solution.

Sample Input 3

4664

Sample Output 3

3498 3498 3498

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Scanner;

public class Main {
    public static void main(String args[]) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        for (long i = 1; i <= 3500; i++) {
            for (long j = i; j <= 3500; j++) {
                long k = lcm(i, j);
                double a = k/i;
                double b = k/j;
                double c = k/N;
                if ((a+b+1) == (4*c)) {
                    System.out.println(i + " " + j + " " + k);
                    return;
                }
            }
        }
    }

    private static long gcd(long a, long b) {
        while (b > 0) {
            long temp = b;
            b = a % b; // % is remainder
            a = temp;
        }
        return a;
    }


    private static long lcm(long a, long b) {
        return a * (b / gcd(a, b));
    }
}