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: Accepted)

#include <bits/stdc++.h>
using namespace std;
#define rep(i, m, n) for (long long i = m; i < n; ++i)

int main() {
    long long N; cin >> N;
    rep(a, 1, 3501) rep(b, 1, 3501) {
        long long u = N * a * b;
        long long d = 4 * a * b - N * b - N * a;
        if(d <= 0) continue;
        long long c = u / d;
        if(c > 0 && c * d == u) {
            cout << a << " " << b << " " << c << endl;
            return 0;
        }
    }
    return 0;
}