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>
#define ll long long
using namespace std;

int main(){

  ll N;
  ll h, n, w;
  ll H, M, W;
  int flag = 1;
  cin >> N;
  for(h = 1; h <= 3500; h++){
    for(n = 1; n <= 3500; n++){
      if((4*h*n-N*n-N*h) == 0 || (N*n*h) % (4*h*n-N*n-N*h) != 0) continue;
      w = (N*n*h) / (4*h*n - N*n - N*h);
      if(w < 0) continue;
      ll tmp = 4 * h * n * w;
      ll tmp1 = N * (n*w + h*w + n*h);
      if(tmp == tmp1){
        H = h;
        M = n;
        W = w;
        flag = 0;
        break;
      }
    }
    if(!flag) break;
  }
  printf("%lld %lld %lld\n", H, M, W);
  return 0;
}