#include using namespace std; #define INF_LL (int64)1e18 #define INF (int32)1e9 #define REP(i, n) for(int64 i = 0;i < (n);i++) #define FOR(i, a, b) for(int64 i = (a);i < (b);i++) #define all(x) x.begin(),x.end() #define fs first #define sc second using int32 = int_fast32_t; using uint32 = uint_fast32_t; using int64 = int_fast64_t; using uint64 = uint_fast64_t; using PII = pair; using PLL = pair; const double eps = 1e-10; templateinline void chmin(A &a, B b){if(a > b) a = b;} templateinline void chmax(A &a, B b){if(a < b) a = b;} template vector make_v(size_t a){return vector(a);} template auto make_v(size_t a,Ts... ts){ return vector(ts...))>(a,make_v(ts...)); } template typename enable_if::value!=0>::type fill_v(U &u,const V... v){u=U(v...);} template typename enable_if::value==0>::type fill_v(U &u,const V... v){ for(auto &e:u) fill_v(e,v...); } template<::std::uint_fast64_t mod> class ModInt{ private: using value_type = ::std::uint_fast64_t; value_type n; public: ModInt() : n(0) {} ModInt(value_type n_) : n(n_ % mod) {} ModInt(const ModInt& m) : n(m.n) {} template explicit operator T() const { return static_cast(n); } value_type get() const { return n; } friend ::std::ostream& operator<<(::std::ostream &os, const ModInt &a) { return os << a.n; } friend ::std::istream& operator>>(::std::istream &is, ModInt &a) { value_type x; is >> x; a = ModInt(x); return is; } bool operator==(const ModInt& m) const { return n == m.n; } bool operator!=(const ModInt& m) const { return n != m.n; } ModInt& operator*=(const ModInt& m){ n = n * m.n % mod; return *this; } ModInt pow(value_type b) const{ ModInt ans = 1, m = ModInt(*this); while(b){ if(b & 1) ans *= m; m *= m; b >>= 1; } return ans; } ModInt inv() const { return (*this).pow(mod-2); } ModInt& operator+=(const ModInt& m){ n += m.n; n = (n < mod ? n : n - mod); return *this; } ModInt& operator-=(const ModInt& m){ n += mod - m.n; n = (n < mod ? n : n - mod); return *this; } ModInt& operator/=(const ModInt& m){ *this *= m.inv(); return *this; } ModInt operator+(const ModInt& m) const { return ModInt(*this) += m; } ModInt operator-(const ModInt& m) const { return ModInt(*this) -= m; } ModInt operator*(const ModInt& m) const { return ModInt(*this) *= m; } ModInt operator/(const ModInt& m) const { return ModInt(*this) /= m; } ModInt& operator++(){ n += 1; return *this; } ModInt& operator--(){ n -= 1; return *this; } ModInt operator++(int){ ModInt old(n); n += 1; return old; } ModInt operator--(int){ ModInt old(n); n -= 1; return old; } ModInt operator-() const { return ModInt(mod-n); } }; template class Matrix{ private: using size_type = ::std::size_t; using Row = ::std::vector; using Mat = ::std::vector; size_type R, C; // row, column Mat A; void add_row_to_another(size_type r1, size_type r2, const T k){ // Row(r1) += Row(r2)*k for(size_type i = 0;i < C;i++) A[r1][i] += A[r2][i]*k; } void scalar_multiply(size_type r, const T k){ for(size_type i = 0;i < C;i++) A[r][i] *= k; } void scalar_division(size_type r, const T k){ for(size_type i = 0;i < C;i++) A[r][i] /= k; } public: Matrix(){} Matrix(size_type r, size_type c) : R(r), C(c), A(r, Row(c)) {} Matrix(const Mat &m) : R(m.size()), C(m[0].size()), A(m) {} Matrix(const Mat &&m) : R(m.size()), C(m[0].size()), A(m) {} Matrix(const Matrix &m) : R(m.R), C(m.C), A(m.A) {} Matrix(const Matrix &&m) : R(m.R), C(m.C), A(m.A) {} Matrix &operator=(const Matrix &m){ R = m.R; C = m.C; A = m.A; return *this; } Matrix &operator=(const Matrix &&m){ R = m.R; C = m.C; A = m.A; return *this; } static Matrix I(const size_type N){ Matrix m(N, N); for(size_type i = 0;i < N;i++) m[i][i] = 1; return m; } const Row& operator[](size_type k) const& { return A.at(k); } Row& operator[](size_type k) & { return A.at(k); } Row operator[](size_type k) const&& { return ::std::move(A.at(k)); } size_type row() const { return R; } // the number of rows size_type column() const { return C; } T determinant(){ assert(R == C); Mat tmp = A; T res = 1; for(size_type i = 0;i < R;i++){ for(size_type j = i;j < R;j++){ // satisfy A[i][i] > 0 if (A[j][i] != 0) { if (i != j) res *= -1; swap(A[j], A[i]); break; } } if (A[i][i] == 0) return 0; res *= A[i][i]; scalar_division(i, A[i][i]); for(size_type j = i+1;j < R;j++){ add_row_to_another(j, i, -A[j][i]); } } swap(tmp, A); return res; } Matrix inverse(){ assert(R == C); assert(determinant() != 0); Matrix inv(Matrix::I(R)), tmp(*this); for(size_type i = 0;i < R;i++){ for(size_type j = i;j < R;j++){ if (A[j][i] != 0) { swap(A[j], A[i]); swap(inv[j], inv[i]); break; } } inv.scalar_division(i, A[i][i]); scalar_division(i, A[i][i]); for(size_type j = 0;j < R;j++){ if(i == j) continue; inv.add_row_to_another(j, i, -A[j][i]); add_row_to_another(j, i, -A[j][i]); } } (*this) = tmp; return inv; } Matrix& operator+=(const Matrix &B){ assert(column() == B.column() && row() == B.row()); for(size_type i = 0;i < R;i++) for(size_type j = 0;j < C;j++) (*this)[i][j] += B[i][j]; return *this; } Matrix& operator-=(const Matrix &B){ assert(column() == B.column() && row() == B.row()); for(size_type i = 0;i < R;i++) for(size_type j = 0;j < C;j++) (*this)[i][j] -= B[i][j]; return *this; } Matrix& operator*=(const Matrix &B){ assert(column() == B.row()); Matrix M(R, B.column()); for(size_type i = 0;i < R;i++) { for(size_type j = 0;j < B.column();j++) { M[i][j] = 0; for(size_type k = 0;k < C;k++) { M[i][j] += (*this)[i][k] * B[k][j]; } } } swap(M, *this); return *this; } Matrix& operator/=(const Matrix &B){ assert(C == B.row()); Matrix M(B); (*this) *= M.inverse(); return *this; } Matrix operator+(const Matrix &B) const { return (Matrix(*this) += B); } Matrix operator-(const Matrix &B) const { return (Matrix(*this) -= B); } Matrix operator*(const Matrix &B) const { return (Matrix(*this) *= B); } Matrix operator/(const Matrix &B) const { return (Matrix(*this) /= B); } bool operator==(const Matrix &B) const { if (column() != B.column() || row() != B.row()) return false; for(size_type i = 0;i < row();i++) for(size_type j = 0;j < column();j++) if ((*this)[i][j] != B[i][j]) return false; return true; } bool operator!=(const Matrix &B) const { return !((*this) == B); } Matrix pow(size_type k){ assert(R == C); Matrix M(Matrix::I(R)); while(k){ if (k & 1) M *= (*this); k >>= 1; (*this) *= (*this); } A.swap(M.A); return *this; } friend ::std::ostream &operator<<(::std::ostream &os, Matrix &p){ for(size_type i = 0;i < p.row();i++){ for(size_type j = 0;j < p.column();j++){ os << p[i][j] << " "; } os << ::std::endl; } return os; } }; constexpr int64 mod = 998244353; using Mint = ModInt; using Mat = Matrix; int64 N, K; inline int64 to_idx(int64 a, int64 b, int64 c) { return a*K*K+b*K+c; } int main(void){ cin.tie(0); ios::sync_with_stdio(false); cin >> N >> K; Mat m(K*K*K, K*K*K), b(K*K*K, 1); REP(i, K) { REP(j, K) { REP(k, K) { m[to_idx(i, j, (k+j)%K)][to_idx(i, j, k)] += 1; m[to_idx(i, (j+i)%K, k)][to_idx(i, j, k)] += 1; m[to_idx((i+1)%K, j, k)][to_idx(i, j, k)] += 1; } } } m.pow(N); b[to_idx(0, 0, 0)][0] = 1; Mat a = m * b; Mint res = 0; REP(i, K) { REP(j, K) { res += a[to_idx(i, j, 0)][0]; } } cout << res << endl; }