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() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);

    int N;
    cin >> N;
    int h, n;
    for (h = 1; h <= 3500; ++h) {
        for (n = 1; n <= 3500; ++n) {
            if (4 * h * n - N * n - N * h <= 0) continue;
            if (N * h *n % (4 * h * n - N * n - N * h) == 0) {
                int w = N * h *n / (4 * h * n - N * n - N * h);
                printf("%d %d %d", h, n, w);
                return 0;
            };
        }
    }
    return 0;
}