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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
int64_t MOD=1000000007;
const long long INF = 1LL<<60;

int main() {
  int64_t N; cin>>N;
  bool finish=false;
  for(int i=1;i<3501;i++){
    for(int j=1;j<3501;j++){
      if((4*i*j-N*i-N*j)>0){
        if((i*j)%(4*i*j-N*i-N*j)==0){
          cout<<i<<' '<<j<<' '<<(i*j)/(4*i*j-N*i-N*j)<<endl;
          finish=true;
          break;
        }
      }
    }
    if(finish) break;
  }  
}