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 ALL(v) (v).begin(), (v).end()
#define rep(i, n) for (ll i = 0, __##i##_length = (n); i < __##i##_length; i++)
#define rep_reverse(i, n) for (ll i = (n)-1; 0 <= i; i--)
#define FOR(i, from, to) for (ll i = (from), __##i##_end = (to); i < __##i##_end; i++)
#define FOR_REVERSE(i, from, to) for (ll i = (to)-1, __##i##_end = (from); __##i##_end <= i; i--)
#define foreach(e, v) for (const auto e : (v))
#define vfree(v) std::vector<int>().swap(v)
#define DEBUG(x) cout << #x << " = " << (x) << endl

using namespace std;
typedef int64_t ll;
typedef vector<ll> llv;
typedef vector<llv> llvv;

ll gcd(ll a, ll b)
{
    return (a < b) ? gcd(b, a) : ((a % b) ? gcd(b, a % b) : b);
}

ll lcm(ll a, ll b)
{
    return a * b / gcd(a, b);
}

int main()
{
    ll N;
    cin >> N;
    rep(a, 3500)
        rep(b, 3500)
    {
        ll A = a + 1;
        ll B = b + 1;
        ll x = N * A * B;
        ll y = 4 * A * B - N * A - N * B;
        if (0 < x && 0 < y && x % y == 0)
        {
            cout << A << " " << B << " " << x / y << endl;
            return 0;
        }
    }
    return 0;
}