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 long ll;
typedef pair<int, int> P;

int MOD=1e9+7;
ll INF=1e18;

int dx[]={1, -1, 0, 0};
int dy[]={0, 0, 1, -1};

int main(){
    ll n; cin>>n;
    for(ll i=1; i<=3500; i++){
        for(ll j=1; j<=3500; j++){
            if(((4*i*j-n*i-n*j)>0) && ((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;
                return 0;
            }
        }
    }
}