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 FOR(v, a, b) for(int v = (a); v < (b); ++v)
#define FORE(v, a, b) for(int v = (a); v <= (b); ++v)
#define REP(v, n) FOR(v, 0, n)
#define REPE(v, n) FORE(v, 0, n)
#define REV(v, a, b) for(int v = (a); v >= (b); --v)
#define RS resize
#define CLR clear
#define PB push_back
#define ALL(x) (x).begin(), (x).end()
#define LLI long long int
using namespace std;

int main(){
  cin.tie(0);
  ios::sync_with_stdio(false);
  
  LLI N;
  cin >> N;

  LLI h,n,w=0;
  for(h=1;h<=3500;++h){
    for(n=1;n<=3500;++n){
      if(4*h*n-N*n-N*h<=0)continue;
      if((N*h*n)%(4*h*n-N*n-N*h) == 0){
	w = (N*h*n)/(4*h*n-N*n-N*h);
	break;
      }
    }
    if(w)break;
  }

  cout << h << " " << n << " " << w << endl;
  
  return 0;
}