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;

using i64 = int_fast64_t;
using f64 = double;

constexpr i64 INF = INT_FAST64_MAX / 2;
constexpr f64 EPS = DBL_EPSILON;

void solve() {
    i64 n;
    cin >> n;
    for (i64 i = 1; i <= 3500; i++) {
        for (i64 j = 1; j <= 3500; j++) {
            i64 k1 = n * i * j;
            i64 k2 = 4 * i * j - n * (i + j);
            if (k2 > 0 && k1 % k2 == 0) {
                cout << i << " " << j << " " << k1 / k2 << endl;
                return;
            }
        }
    }
}

int main() {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(15);
    solve();
}