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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

int main(int argc, char *argv[])
{
    int N;
    cin >> N;

    for(int h = 1; h <= 5000; ++h)
    {
        for(int n = 1; n <= 5000; ++n)
        {
            int top = N*h*n;
            int bottom = 4 * h * n - N * (n + h);

            if(bottom == 0) continue;

            int w = top / bottom;
            if(w <= 0) continue;

            if((top / bottom) * bottom == top)
            {
                cout << h << ' ' << n << ' ' << w << endl;
                return 0;
            }
        }
    }
}