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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;

typedef pair<int, int> PII;
typedef map<int, int> MII;
typedef priority_queue<int> P_QI;
typedef priority_queue<string> P_QS;
typedef vector<int> VI;
typedef vector<long long> VLL;
typedef vector< int > :: iterator $$;

#define $ vector< int > :: iterator

#define m_p make_pair
#define p_b push_back
#define rep(i, n) for(int i=0; i<(n); i++)
#define forn(i, a, n) for (int i = (int)(a); i < (int)(n); ++i)
#define ford(i, a, n) for (int i = (int)(n - 1); i >= (int)(a); --i)
#define fore(i, a, n) for (int i = (int)(a); i <= (int)(n); ++i)

#define forv(i,v) rep(i,SZ(v))
#define forit(i,s) for(auto i=(s).begin();i!=(s).end();++i)

#define Boost ios_base::sync_with_stdio(0); cin.tie(0)
#define all(a) (a).begin(), (a).end()
#define SZ(x) ((int)(x).size())
#define F first
#define S second
#define _ <<" "<<
#define CS(i) cout<<"Case "<<(int)(i)<<": "

const int MOD = 1e9+7;
const int inf = 1e9+9;
const long long INF = 1e18+3;
const ld eps = 1e-9;
const ld PI=acos(-1.0);


int main() {
Boost;
    ull n,a,b=1,x,y,z,A;
    cin>>n;
    int m=n%4;
    for(int i=4-m;(int)n+i<=4*3500;i=i+4){
      b=n*n/i;
      if(i*b==n*n && (n+b)%4==0) { x=(n+i)/4; A=(n+b)/4; break; }

    }
    for(ull i=1;i<=A;i++){
        z=A*A/i;
        if(z*i==A*A) { y=A+i; z+=A; break;}
    }
    cout<<x _ y _ z<<endl;
return 0;
}