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 <iostream>
#include <math.h>
using namespace std;
typedef long long ll;

int main(void){
    ll n;
    cin >> n;
    
    for (ll i = 1; i <= 3500; i++) {
        for (ll j = 1; j <= 3500; j++) {
            ll low = 0, high = 3500;
            while (high - low > 1) {
                int k = (low + high) / 2;
                if (4 * i * j * k >= n * (i*j + j*k + k*i)) high = k;
                else low = k;
            }
            
            //cout << i << " " << j << " " << high << endl;
            if (4 * i * j * high == n * (i*j + j*high + high*i)) {
                cout << i << " " << j << " " << high << endl;
                return 0;
            }
        }
    }
    
}