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 int long long
#define pii pair<int,int>
#define pb push_back
#define ub upper_bound
#define lb lower_bound
#define all(x) x.begin(),x.end()
#define ld long double
#define fast  ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
using namespace std;
signed main(){
    fast;
    int N;
    cin>>N;
    for(int w = 1;w<=3500;w++){
        for(int h = 1;h<=3500;h++){
            int num = N*w*h;
            int den = (int)4*w*h - N*(w+h);
            if(den>0){
                if(num%den == 0 && (num/den)<=3500){
                    cout<<h<<" "<<num/den<<" "<<w;
                    return 0;
                }
            }
        }
    }
}