#include #include #include #include template struct Matrix : public std::vector> { // constructor using std::vector>::vector; Matrix(int h, int w, T val = 0) { this->resize(h); for (auto& v : *this) v.resize(w, val); } static Matrix id(int n) { Matrix m(n, n); for (int i = 0; i < n; ++i) m[i][i] = 1; return m; } // arithmetic Matrix operator*(const Matrix& m) const { return Matrix(*this) *= m; } Matrix& operator*=(const Matrix& m) { int h1 = this->size(), h2 = m.size(), w2 = m.front().size(); Matrix nmat(h1, w2); for (int i = 0; i < h1; ++i) { for (int j = 0; j < w2; ++j) { for (int k = 0; k < h2; ++k) { nmat[i][j] += (*this)[i][k] * m[k][j]; } } } return *this = nmat; } template Matrix pow(U k) { Matrix ret = id(this->size()); Matrix a = *this; while (k > 0) { if (k & 1) ret *= a; a *= a; k >>= 1; } return ret; } }; using namespace std; using mint = atcoder::modint998244353; bool judge(int i, int j, int k) { return ((i > j && j < k) || (i < j && j > k)) && i != k; } void solve() { int n, m; cin >> n >> m; auto enc = [&](int i, int j) { return i * m + j; }; int nn = m * m; Matrix mat(nn * 2, nn * 2); for (int i = 0; i < m; ++i) { for (int j = 0; j < m; ++j) { for (int k = 0; k < m; ++k) { if (!judge(i, j, k)) continue; int s = enc(i, j), t = enc(j, k); mat[t][s] = 1; mat[t + nn][s + nn] = 1; mat[t + nn][s] = k; } } } mat = mat.pow(n - 2); vector vec(nn * 2, 0); for (int i = 0; i < m; ++i) { for (int j = 0; j < m; ++j) { if (i == j) continue; vec[enc(i, j)] = 1; vec[enc(i, j) + nn] = i + j; } } mint cans = 0, sans = 0; for (int i = 0; i < nn * 2; ++i) { mint s = 0; for (int j = 0; j < nn * 2; ++j) { s += mat[i][j] * vec[j]; } (i < nn ? cans : sans) += s; } cout << cans.val() << " " << sans.val() << "\n"; } int main() { cin.tie(nullptr); ios::sync_with_stdio(false); solve(); return 0; }