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;
#define inf 1e9
#define ll long long
#define ull unsigned long long
#define M 1000000007
#define P pair<int,int>
#define FOR(i,m,n) for(int i=m;i<n;i++)
#define rep(i,n) FOR(i,0,n)
const int vx[4] = {0,1,0,-1};
const int vy[4] = {1,0,-1,0};
#define PI 3.14159265

int N;

int main(){
  cin>>N;

  for(ll i=1;i<3501;i++){
    for(ll j=1;j<3501;j++){
      if(4*i*j-N*i-N*j<=0) continue;
      if((N*i*j)%(4*i*j-N*i-N*j)==0){
        cout<<i<<' '<<j<<' '<<(N*i*j)/(4*i*j-N*i-N*j)<<endl;
        goto ABC;
      }
    }
  }

  ABC:

  return 0;
}