typedef vector<vector<ll>> matrix;
matrix matrixProduct(matrix a, matrix b) {
    if (!a.size() || !b.size()) return {};
    if (a[0].size() != b.size()) return {};
    ll n = a.size();
    ll m = b[0].size();
    matrix res(n, vector<ll>(m, 0));
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < m; j++) {
            for (int k = 0; k < a[0].size(); k++) {
                res[i][j] += a[i][k] * b[k][j];
                res[i][j] %= mod;
            }
        }
    }
    return res;
}

matrix operator*(const matrix &a, matrix &b) {
    return matrixProduct(a, b);
}

matrix binpow(matrix a, ll k) {
    int n = a.size();
    int m = a[0].size();
    matrix res(n, vector<ll>(m));
    if (k == 0) {
        for (int i = 0; i < n; i++) {
            res[i][i] = 1;
        }
        return res;
    }
    res = a;
    k--;
    while (k) {
        if (k & 1) res = res * a;
        a = a * a;
        k >>= 1;
    }
    return res;
}