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

int calc(int n, int m, int k)
{
    if (n*m%k) return 0;
    unordered_set<string> ans;
    vector<int> v;
    int bins = n*m/k;
    for (int i = 0; i < m; i++) for (int j = 0; j < n; j++) v.push_back(i);
    do
    {
        vector<string> cur;
        for (int i = 0; i < bins; i++)
        {
            string bin;
            for (int j = i*k; j < i*k+k; j++) bin += 1+v[j];
            sort(bin.begin(), bin.end());
            cur.push_back(bin);
        }
        sort(cur.begin(), cur.end());
        string f;
        for (auto &u : cur) f += u;
        ans.insert(f);
    } while (next_permutation(v.begin(), v.end()));
    return ans.size();
}

int main()
{
    const int colWidth = 8, N = 4, M = 4, K = 6;
    auto start = chrono::high_resolution_clock::now();
    for (int k = 2; k <= K; k++)
    {
        cout << "\nk=" << k << "\n\n";

        cout << setw(colWidth) << " ";
        for (int n = 1; n <= N; n++) cout << setw(colWidth) << "n=" + to_string(n);
        cout << '\n';

        for (int m = 2; m <= M; m++)
        {
            cout << setw(colWidth) << "m=" + to_string(m);
            for (int n = 1; n <= N; n++) cout << setw(colWidth) << calc(n, m, k);
            cout << '\n';
        }
    }

    auto stop = chrono::high_resolution_clock::now();
    cout << "\nTime taken: " << chrono::duration_cast<chrono::seconds>(stop-start);
}