#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using ll = long long; #define fst first #define snd second /* clang-format off */ template struct _vec { using type = vector::type>; }; template struct _vec { using type = T; }; template using vec = typename _vec::type; template vector make_v(size_t size, const T &init) { return vector(size, init); } template auto make_v(size_t size, Ts... rest) { return vector(size, make_v(rest...)); } template inline void chmin(T &a, const T &b) { if (b < a) a = b; } template inline void chmax(T &a, const T &b) { if (b > a) a = b; } /* clang-format on */ using vi = vector; //@formatter:off template T minv(T a, T m); template T minv(T a); template class Modular { public: using Type = typename decay::type; constexpr Modular() : value() {} template Modular(const U &x) { value = normalize(x); } template static Type normalize(const U &x) { Type v; if (-mod() <= x && x < mod()) v = static_cast(x); else v = static_cast(x % mod()); if (v < 0) v += mod(); return v; } const Type &operator()() const { return value; } templateexplicit operator U() const { return static_cast(value); } constexpr static Type mod() { return T::value; } Modular &operator+=(const Modular &other) { if ((value += other.value) >= mod()) value -= mod(); return *this; } Modular &operator-=(const Modular &other) { if ((value -= other.value) < 0) value += mod(); return *this; } template Modular &operator+=(const U &other) { return *this += Modular(other); } template Modular &operator-=(const U &other) { return *this -= Modular(other); } Modular &operator++() { return *this += 1; } Modular &operator--() { return *this -= 1; } Modular operator++(signed) { Modular result(*this); *this += 1; return result; } Modular operator--(signed) { Modular result(*this); *this -= 1; return result; } Modular operator-() const { return Modular(-value); } templatetypename enable_if::Type, signed>::value, Modular>::type &operator*=(const Modular &rhs) { #ifdef _WIN32 uint64_t x = static_cast(value) * static_cast(rhs.value);uint32_t xh = static_cast(x >> 32), xl = static_cast(x), d, m;asm("divl %4; \n\t": "=a" (d), "=d" (m): "d" (xh), "a" (xl), "r" (mod()));value = m; #else value = normalize(static_cast(value) * static_cast(rhs.value)); #endif return *this; } template typename enable_if::Type, int64_t>::value, Modular>::type &operator*=(const Modular &rhs) { int64_t q = static_cast(static_cast(value) * rhs.value / mod()); value = normalize(value * rhs.value - q * mod()); return *this; } template typename enable_if::Type>::value, Modular>::type &operator*=(const Modular &rhs) { value = normalize(value * rhs.value); return *this; } Modular &operator/=(const Modular &other) { return *this *= Modular(minv(other.value)); } template friend bool operator==(const Modular &lhs, const Modular &rhs); template friend bool operator<(const Modular &lhs, const Modular &rhs); template friend std::istream &operator>>(std::istream &stream, Modular &number); operator int() { return value; }private: Type value; }; template bool operator==(const Modular &lhs, const Modular &rhs) { return lhs.value == rhs.value; }template bool operator==(const Modular &lhs, U rhs) { return lhs == Modular(rhs); }template bool operator==(U lhs, const Modular &rhs) { return Modular(lhs) == rhs; }template bool operator!=(const Modular &lhs, const Modular &rhs) { return !(lhs == rhs); }template bool operator!=(const Modular &lhs, U rhs) { return !(lhs == rhs); }template bool operator!=(U lhs, const Modular &rhs) { return !(lhs == rhs); }template bool operator<(const Modular &lhs, const Modular &rhs) { return lhs.value < rhs.value; }template Modular operator+(const Modular &lhs, const Modular &rhs) { return Modular(lhs) += rhs; }template Modular operator+(const Modular &lhs, U rhs) { return Modular(lhs) += rhs; }template Modular operator+(U lhs, const Modular &rhs) { return Modular(lhs) += rhs; }template Modular operator-(const Modular &lhs, const Modular &rhs) { return Modular(lhs) -= rhs; }template Modular operator-(const Modular &lhs, U rhs) { return Modular(lhs) -= rhs; }template Modular operator-(U lhs, const Modular &rhs) { return Modular(lhs) -= rhs; }template Modular operator*(const Modular &lhs, const Modular &rhs) { return Modular(lhs) *= rhs; }template Modular operator*(const Modular &lhs, U rhs) { return Modular(lhs) *= rhs; }template Modular operator*(U lhs, const Modular &rhs) { return Modular(lhs) *= rhs; }template Modular operator/(const Modular &lhs, const Modular &rhs) { return Modular(lhs) /= rhs; }template Modular operator/(const Modular &lhs, U rhs) { return Modular(lhs) /= rhs; }template Modular operator/(U lhs, const Modular &rhs) { return Modular(lhs) /= rhs; } constexpr signed MOD = 998244353; //1e9 + 7;//MOD using mint = Modular::type, MOD>>; constexpr int mint_len = 1400001; vi fac, finv, inv; vi p2; mint com(int n, int r) { if (r < 0 || r > n) return 0; return mint(finv[r] * fac[n] % MOD * finv[n - r]);} mint pom(int n, int r) {/* if (!sz(fac)) com(0, -1);*/ if (r < 0 || r > n) return 0; return mint(fac[n] * finv[n - 1]);} mint npr(int n, int r) {/* if (!sz(fac)) com(0, -1);*/ if (r < 0 || r > n) return 0; return mint(fac[n] * finv[n - r]);} int nprin(int n, int r) {/* if (!sz(fac)) com(0, -1);*/ if (r < 0 || r > n) return 0; return fac[n] * finv[n - r] % MOD;} int icom(int n, int r) { const int NUM_ = 1400001; static ll fac[NUM_ + 1], finv[NUM_ + 1], inv[NUM_ + 1]; if (fac[0] == 0) { inv[1] = fac[0] = finv[0] = 1; for (int i = 2; i <= NUM_; ++i) inv[i] = inv[MOD % i] * (MOD - MOD / i) % MOD; for (int i = 1; i <= NUM_; ++i) fac[i] = fac[i - 1] * i % MOD, finv[i] = finv[i - 1] * inv[i] % MOD; } if (r < 0 || r > n) return 0; return ((finv[r] * fac[n] % MOD) * finv[n - r]) % MOD;} #define ncr com #define ncri icom //n個の場所にr個の物を置く mint nhr(int n, int r) { return com(n + r - 1, r); } mint hom(int n, int r) { return com(n + r - 1, r); } int nhri(int n, int r) { return icom(n + r - 1, r); } template T minv(T a, T m) { T u = 0, v = 1; while (a != 0) { T t = m / a; m -= t * a; swap(a, m); u -= t * v; swap(u, v); } assert(m == 1); return u;} template T minv(T a) { if (a < mint_len)return inv[a]; T u = 0, v = 1; T m = MOD; while (a != 0) { T t = m / a; m -= t * a; swap(a, m); u -= t * v; swap(u, v); } assert(m == 1); return u;} template Modular mpow(const Modular &a, const U &b) { assert(b >= 0); int x = a(), res = 1; U p = b; while (p > 0) { if (p & 1) (res *= x) %= MOD; (x *= x) %= MOD; p >>= 1; } return res;} template mint mpow(const T a, const U b, const V m = MOD) { assert(b >= 0); int x = a, res = 1; U p = b; while (p > 0) { if (p & 1) (res *= x) %= m; (x *= x) %= m; p >>= 1; } return res;} template mint mpow(const T a, const U b) { assert(b >= 0); int x = a, res = 1; U p = b; while (p > 0) { if (p & 1) (res *= x) %= MOD; (x *= x) %= MOD; p >>= 1; } return res;} template int mpowi(const T &a, const U &b, const V &m = MOD) { assert(b >= 0); int x = a, res = 1; U p = b; while (p > 0) { if (p & 1) (res *= x) %= m; (x *= x) %= m; p >>= 1; } return res;} template string to_string(const Modular &number) { return to_string(number());} template std::ostream &operator<<(std::ostream &stream, const Modular &number) { return stream << number();} template std::istream &operator>>(std::istream &stream, Modular &number) { typename common_type::Type, int64_t>::type x; stream >> x; number.value = Modular::normalize(x); return stream;} //using mint = modint<998244353>; typedef vector Vec; typedef vector Mat; Mat eye(int n) { Mat I(n, Vec(n)); for (int i = 0; i < n; ++i) I[i][i] = 1; return I; } Mat mul(Mat A, const Mat &B) { for (int i = 0; i < A.size(); ++i) { Vec x(A[0].size()); for (int k = 0; k < B.size(); ++k) for (int j = 0; j < B[0].size(); ++j) x[j] += A[i][k] * B[k][j]; A[i].swap(x); } return A; } Mat pow(Mat A, ll k) { Mat X = eye(A.size()); for (; k > 0; k /= 2) { if (k & 1) X = mul(X, A); A = mul(A, A); } return X; } Vec mul(const Mat &A, const Vec &b) { Vec y(A.size()); for (int i = 0; i < A.size(); ++i) for (int j = 0; j < A[0].size(); ++j) y[i] += A[i][j] * b[j]; return y; } ll solveNaive(int N, int K) { vec dp = make_v(K, K, K, mint(0)); dp[0][0][0] = 1; for (int t = 0; t < N; t++) { vec ndp = make_v(K, K, K, mint(0)); for (int a = 0; a < K; a++) { for (int b = 0; b < K; b++) { for (int c = 0; c < K; c++) { mint cur = dp[a][b][c]; ndp[(a + 1) % K][b][c] += cur; ndp[a][(a + b) % K][c] += cur; ndp[a][b][(b + c) % K] += cur; } } } dp = ndp; } mint res = 0; for (int a = 0; a < K; a++) for (int b = 0; b < K; b++) res += dp[a][b][0]; return res; } ll solve(int N, int K) { int dim = K * K * K; auto encode = [&](int a, int b, int c) { return a * K * K + b * K + c; }; Mat A = make_v(dim, dim, mint(0)); for (int a = 0; a < K; a++) { for (int b = 0; b < K; b++) { for (int c = 0; c < K; c++) { int cur = encode(a, b, c); A[encode((a + 1) % K, b, c)][cur] += 1; A[encode(a, (a + b) % K, c)][cur] += 1; A[encode(a, b, (b + c) % K)][cur] += 1; } } } A = pow(A, N); Vec init(dim); init[0] = 1; auto goal = mul(A, init); mint res = 0; for (int a = 0; a < K; a++) { for (int b = 0; b < K; b++) { res += goal[encode(a, b, 0)]; } } return res; } int main() { #ifdef DEBUG ifstream ifs("in.txt"); cin.rdbuf(ifs.rdbuf()); #endif int N, K; while (cin >> N >> K) { cout << solve(N, K) << endl; } return 0; }