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 <bits/stdc++.h>
#include <time.h>
#include <sys/timeb.h>
#include <cstdio>
#include <sys/time.h>

using namespace std;
#define ll long long
#define uint unsigned int
#define ulong unsigned long long int

template<typename T> bool InRange(T t, T l, T r){ return l <= t && t < r; }

int main(){
	
	ll N;
	cin >> N;
	
	for(ll h = 1; h <= 3500; h++){
		for(ll w = 1; w <= 3500; w++){
			ll left = 4 * h * w - N * w - N * h;
			ll right = N * h * w;
			if(left > 0 && right % left == 0){
				ll n = right / left;
				cout << h << " " << n << " " << w << endl;
				return 0;
			}
			
			
		}
	
	}
	
	
	
	
	
    return 0;
}