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;

typedef long double ld;

int main()
{
	ld N;
	cin >> N;
	for(ld i=1;i<=3500;i+=1)
	{
		for(ld j=1;j<=3500;j+=1)
		{
			if(4*i*j-N*j-N*i==0)
				continue;
			ld w=(N*i*j)/(4*i*j-N*j-N*i);
			if(w==(long long)w&&w>0)
			{
				printf("%.0Lf %.0Lf %.0Lf\n",i,j,w);
				return 0;
			}
		}
	}
	return 0;
}