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

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

int main() {
    int N;
    cin >> N;
    
    for(int n = 1; n <= 3500; n++){
        for(int w = 1; w <= 3500; w++){
            unsigned long long int h_up, h_down;
            h_up = N * n * w;
            h_down = 4 * n * w - N *(n + w);
            
            if(h_down <= 0) continue;
            if(h_up % h_down != 0) continue;
            //cout << h_up << " " << h_down << endl;
            
            unsigned long long int h;
            h = h_up / h_down;
            
            if(3500 < h) continue;
            
            cout << h << " " << n << " " << w << endl;
            exit(0);
        }
    }
}