12470 - Tribonacci

/*
+---------------------------------------------+
|                                             |
|       © 29/01/2024 (15:37) MinaMagdy        |
|                                             |
+---------------------------------------------+
*/
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;
#define ordered_set tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update>
#define multi_ordered_set tree<int, null_type, less_equal<int>, rb_tree_tag, tree_order_statistics_node_update>
#define endl "\n"
#define MOD 1000000007
#define INF 2000000000
#define all(s) s.begin(), s.end()
#define rall(s) s.rbegin(), s.rend()
#define sz(x) int(x.size())

typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
#include <ext/numeric>
using namespace __gnu_cxx;
const int mod = 1000000009;
typedef vector<vector<int>> matrix;
struct mul
{
    int n;
    mul(int n) : n(n) {}
    matrix operator()(const matrix &a, const matrix &b)
    {
        assert(a[0].size() == b.size());
        matrix c(a.size(), vector<int>(b[0].size(), 0));
        for (int i = 0; i < a.size(); i++)
        {
            for (int j = 0; j < b[0].size(); j++)
            {
                for (int k = 0; k < b.size(); k++)
                {
                    c[i][j] += a[i][k] * 1ll * b[k][j] % mod;
                    if (c[i][j] >= mod)
                        c[i][j] -= mod;
                }
            }
        }
        return c;
    }
};

matrix identity_element(const mul &m)
{
    matrix res(m.n, vector<int>(m.n, 0));
    for (int i = 0; i < m.n; i++)
        res[i][i] = 1;
    return res;
}

void solve()
{
    ll n;
    while (cin >> n, n)
    {
        matrix m = {
            {0, 1, 0},
            {0, 0, 1},
            {1, 1, 1}};
        matrix f1 = {
            {0},
            {1},
            {2}};
        mul mm(3);
        cout << mm(power(m, n - 1, mm), f1)[0][0] << endl;
    }
}

int main(void)
{
    ios_base::sync_with_stdio(false), cin.tie(NULL), cout.tie(NULL);
    int testcase = 1;
    // cin >> testcase;
    while (testcase--)
        solve();
    return 0;
}