#include #pragma GCC diagnostic ignored "-Wsign-compare" #pragma GCC diagnostic ignored "-Wsign-conversion" #define NDEBUG #define SHOW(...) static_cast(0) //!===========================================================!// //! dP dP dP !// //! 88 88 88 !// //! 88aaaaa88a .d8888b. .d8888b. .d888b88 .d8888b. 88d888b. !// //! 88 88 88ooood8 88' '88 88' '88 88ooood8 88' '88 !// //! 88 88 88. ... 88. .88 88. .88 88. ... 88 !// //! dP dP '88888P' '88888P8 '88888P8 '88888P' dP !// //!===========================================================!// template std::istream& operator>>(std::istream& is, std::vector& v) { for (auto& e : v) { is >> e; } return is; } template T read() { T v; return std::cin >> v, v; } template std::vector readVec(const std::size_t l) { std::vector v(l); for (auto& e : v) { std::cin >> e; } return v; } using ld = long double; using uint = unsigned int; using ll = long long; using ull = unsigned long long; constexpr unsigned int MOD = 1000000007; template constexpr T INF = std::numeric_limits::max() / 4; template constexpr F PI = static_cast(3.1415926535897932385); std::mt19937 mt{std::random_device{}()}; template bool chmin(T& a, const T& b) { return (a > b ? a = b, true : false); } template bool chmax(T& a, const T& b) { return (a < b ? a = b, true : false); } template std::vector Vec(const std::size_t n, T v) { return std::vector(n, v); } template auto Vec(const std::size_t n, Args... args) { return std::vector(n, Vec(args...)); } template constexpr T popCount(const T u) { #ifdef __has_builtin return u == 0 ? T(0) : (T)__builtin_popcountll(u); #else unsigned long long v = static_cast(u); return v = (v & 0x5555555555555555ULL) + (v >> 1 & 0x5555555555555555ULL), v = (v & 0x3333333333333333ULL) + (v >> 2 & 0x3333333333333333ULL), v = (v + (v >> 4)) & 0x0F0F0F0F0F0F0F0FULL, static_cast(v * 0x0101010101010101ULL >> 56 & 0x7f); #endif } template constexpr T log2p1(const T u) { #ifdef __has_builtin return u == 0 ? T(0) : T(64 - __builtin_clzll(u)); #else unsigned long long v = static_cast(u); return v = static_cast(v), v |= (v >> 1), v |= (v >> 2), v |= (v >> 4), v |= (v >> 8), v |= (v >> 16), v |= (v >> 32), popCount(v); #endif } template constexpr T clog(const T v) { return v == 0 ? T(0) : log2p1(v - 1); } template constexpr T msbp1(const T v) { return log2p1(v); } template constexpr T lsbp1(const T v) { #ifdef __has_builtin return __builtin_ffsll(v); #else return v == 0 ? T(0) : popCount((v & (-v)) - T(1)) + T(1); #endif } template constexpr bool ispow2(const T v) { return popCount(v) == 1; } template constexpr T ceil2(const T v) { return v == 0 ? T(1) : T(1) << log2p1(v - 1); } template constexpr T floor2(const T v) { return v == 0 ? T(0) : T(1) << (log2p1(v) - 1); } //!===============================================================!// //! 88888888b dP .88888. a88888b. 888888ba !// //! 88 88 d8' '88 d8' '88 88 '8b !// //! a88aaaa dP. .dP d8888P 88 88 88 88 !// //! 88 '8bd8' 88 88 YP88 88 88 88 !// //! 88 .d88b. 88 Y8. .88 Y8. .88 88 .8P !// //! 88888888P dP' 'dP dP '88888' Y88888P' 8888888P !// //!===============================================================!// template constexpr std::pair extgcd(const T a, const T b) { if (b == 0) { return std::pair{1, 0}; } const auto p = extgcd(b, a % b); return {p.second, p.first - p.second * (a / b)}; } template constexpr T inverse(const T a, const T mod) { return (mod + extgcd((mod + a % mod) % mod, mod).first % mod) % mod; } //!========================================================!// //! 8888ba.88ba dP dP dP !// //! 88 '8b '8b 88 88 88 !// //! 88 88 88 .d8888b. .d888b88 88 88d888b. d8888P !// //! 88 88 88 88' '88 88' '88 88 88' '88 88 !// //! 88 88 88 88. .88 88. .88 88 88 88 88 !// //! dP dP dP '88888P' '88888P8 dP dP dP dP !// //!========================================================!// template class ModInt { private: uint v; static uint norm(const uint& x) { return x < mod ? x : x - mod; } static ModInt make(const uint& x) { ModInt m; return m.v = x, m; } static ModInt power(ModInt x, ll n) { ModInt ans = 1; for (; n; n >>= 1, x *= x) { if (n & 1) { ans *= x; } } return ans; } static ModInt inv(const ModInt& x) { return ModInt{inverse((ll)x.v, (ll)mod)}; } public: ModInt() : v{0} {} ModInt(const ll val) : v{norm(uint(val % (ll)mod + (ll)mod))} {} ModInt(const ModInt& n) : v{n()} {} explicit operator bool() const { return v != 0; } ModInt& operator=(const ModInt& n) { return v = n(), (*this); } ModInt& operator=(const ll val) { return v = norm(uint(val % (ll)mod + (ll)mod)), (*this); } ModInt operator+() const { return *this; } ModInt operator-() const { return make(norm(mod - v)); } ModInt operator+(const ModInt& val) const { return make(norm(v + val())); } ModInt operator-(const ModInt& val) const { return make(norm(v + mod - val())); } ModInt operator*(const ModInt& val) const { return make((uint)((ll)v * val() % (ll)mod)); } ModInt operator/(const ModInt& val) const { return *this * inv(val()); } ModInt& operator+=(const ModInt& val) { return *this = *this + val; } ModInt& operator-=(const ModInt& val) { return *this = *this - val; } ModInt& operator*=(const ModInt& val) { return *this = *this * val; } ModInt& operator/=(const ModInt& val) { return *this = *this / val; } ModInt operator+(const ll val) const { return ModInt{v + val}; } ModInt operator-(const ll val) const { return ModInt{v - val}; } ModInt operator*(const ll val) const { return ModInt{(ll)v * (val % mod)}; } ModInt operator/(const ll val) const { return ModInt{(ll)v * inv(val)}; } template ModInt operator^(const I n) const { return power(v, n); } ModInt& operator+=(const ll val) { return *this = *this + val; } ModInt& operator-=(const ll val) { return *this = *this - val; } ModInt& operator*=(const ll val) { return *this = *this * val; } ModInt& operator/=(const ll val) { return *this = *this / val; } template ModInt& operator^=(const I n) { return (*this) = ((*this) ^ n); } bool operator==(const ModInt& val) const { return v == val.v; } bool operator!=(const ModInt& val) const { return not(*this == val); } bool operator==(const ll val) const { return v == norm(uint((ll)mod + val % (ll)mod)); } bool operator!=(const ll val) const { return not(*this == val); } uint operator()() const { return v; } }; template inline ModInt operator+(const ll val, const ModInt& n) { return n + val; } template inline ModInt operator-(const ll val, const ModInt& n) { return ModInt{val - (ll)n()}; } template inline ModInt operator*(const ll val, const ModInt& n) { return n * val; } template inline ModInt operator/(const ll val, const ModInt& n) { return ModInt(val) / n; } template inline bool operator==(const ll val, const ModInt& n) { return n == val; } template inline bool operator!=(const ll val, const ModInt& n) { return not(val == n); } template inline std::istream& operator>>(std::istream& is, ModInt& n) { uint v; return is >> v, n = v, is; } template std::ostream& operator<<(std::ostream& os, const ModInt& n) { return (os << n()); } //!=====================================================!// //! 8888ba.88ba dP oo !// //! 88 '8b '8b 88 !// //! 88 88 88 .d8888b. d8888P 88d888b. dP dP. .dP !// //! 88 88 88 88' '88 88 88' '88 88 '8bd8' !// //! 88 88 88 88. .88 88 88 88 .d88b. !// //! dP dP dP '88888P8 dP dP dP dP' 'dP !// //!=====================================================!// template struct Matrix { Matrix(const std::size_t R, const std::size_t C) : R{R}, C{C}, table(R, std::vector(C, T(0))) {} const std::vector& operator[](const std::size_t r) const { return table[r]; } std::vector& operator[](const std::size_t r) { return table[r]; } Matrix operator-() const { Matrix ans(R, C); for (std::size_t i = 0; i < R; i++) { for (std::size_t j = 0; j < C; j++) { ans[i][j] = -table[i][j]; } } return ans; } Matrix operator+(const Matrix& m) const { assert(R == m.R); assert(C == m.C); Matrix ans(R, C); for (std::size_t i = 0; i < R; i++) { for (std::size_t j = 0; j < C; j++) { ans[i][j] = table[i][j] + m[i][j]; } } return ans; } Matrix operator-(const Matrix& m) const { assert(R == m.R); assert(C == m.C); Matrix ans(R, C); for (std::size_t i = 0; i < R; i++) { for (std::size_t j = 0; j < C; j++) { ans[i][j] = table[i][j] - m[i][j]; } } return ans; } Matrix operator*(const Matrix& m) const { assert(C == m.R); Matrix ans(R, m.C); for (std::size_t i = 0; i < R; i++) { for (std::size_t j = 0; j < m.C; j++) { for (std::size_t k = 0; k < C; k++) { ans[i][j] += table[i][k] * m[k][j]; } } } return ans; } Matrix operator*(const T& t) const { Matrix ans(R, C); for (std::size_t i = 0; i < R; i++) { for (std::size_t j = 0; j < C; j++) { ans[i][j] = table[i][j] * t; } } return ans; } template Matrix operator^(const C n) const { return assert(n > 0), n == 1 ? *this : n % 2 == 1 ? (*this) * ((*this) ^ (n - 1)) : (((*this) * (*this)) ^ (n / 2)); } Matrix& operator=(const Matrix& m) { assert(R == m.R); assert(C == m.C); for (std::size_t i = 0; i < R; i++) { for (std::size_t j = 0; j < C; j++) { table[i][j] = m[i][j]; } } return *this; } Matrix& operator+=(const Matrix& m) { assert(R == m.R); assert(C == m.C); for (std::size_t i = 0; i < R; i++) { for (std::size_t j = 0; j < C; j++) { table[i][j] += m[i][j]; } } } Matrix& operator-=(const Matrix& m) { assert(R == m.R); assert(C == m.C); for (std::size_t i = 0; i < R; i++) { for (std::size_t j = 0; j < C; j++) { table[i][j] -= m[i][j]; } } return *this; } Matrix& operator*=(const Matrix& m) { return *this = (*this) * m; } Matrix& operator*=(const T& t) { for (std::size_t i = 0; i < R; i++) { for (std::size_t j = 0; j < C; j++) { table[i][j] *= t; } } return *this; } template Matrix& operator^=(const C n) { return (*this) = ((*this) ^ n); } const std::size_t R, C; std::vector> table; }; template Matrix operator*(const T& t, const Matrix& m) { return m * t; } template std::ostream& operator<<(std::ostream& os, const Matrix& m) { os << "[\n"; for (std::size_t i = 0; i < m.R; i++) { os << "["; for (std::size_t j = 0; j < m.C; j++) { os << m[i][j] << " "; } os << "]\n"; } return (os << "]\n"); } template struct Vector { Vector(const std::size_t R) : R{R}, table(R, T(0)) {} const T& operator[](const std::size_t r) const { return table[r]; } T& operator[](const std::size_t r) { return table[r]; } Vector operator+(const Vector& v) const { assert(R == v.R); Vector ans(R); for (std::size_t i = 0; i < R; i++) { ans[i] = table[i] + v[i]; } return ans; } Vector operator-(const Vector& v) const { assert(R == v.R); Vector ans(R); for (std::size_t i = 0; i < R; i++) { ans[i] = table[i] - v[i]; } return ans; } Vector operator*(const T& t) const { Vector ans(R); for (std::size_t i = 0; i < R; i++) { ans[i] = table[i] * t; } return ans; } Vector& operator=(const Vector& v) { assert(R == v.R); for (std::size_t i = 0; i < R; i++) { table[i] = v[i]; } return *this; } Vector& operator+=(const Vector& v) { assert(R == v.R); for (std::size_t i = 0; i < R; i++) { table[i] += v[i]; } return *this; } Vector& operator-=(const Vector& v) { assert(R == v.R); for (std::size_t i = 0; i < R; i++) { table[i] -= v[i]; } return *this; } Vector& operator*=(const T& t) { Vector ans(R); for (std::size_t i = 0; i < R; i++) { table[i] *= t; } return *this; } const std::size_t R; std::vector table; }; template Vector operator*(const T& t, const Vector& v) { return v * t; } template Vector operator*(const Matrix& m, const Vector& v) { assert(m.C == v.R); Vector ans(m.R); for (std::size_t i = 0; i < m.R; i++) { for (std::size_t j = 0; j < m.C; j++) { ans[i] += m[i][j] * v[j]; } } return ans; } template std::ostream& operator<<(std::ostream& os, const Vector& v) { os << "[\n"; for (std::size_t i = 0; i < v.R; i++) { os << v[i] << "\n"; } return (os << "]\n"); } template struct TVector { TVector(const std::size_t C) : C{C}, table(C, T(0)) {} const T& operator[](const std::size_t c) const { return table[c]; } T& operator[](const std::size_t c) { return table[c]; } TVector operator+(const TVector& v) const { assert(C == v.C); TVector ans(C); for (std::size_t i = 0; i < C; i++) { ans[i] = table[i] + v[i]; } return ans; } TVector operator-(const TVector& v) const { assert(C == v.C); TVector ans(C); for (std::size_t i = 0; i < C; i++) { ans[i] = table[i] - v[i]; } return ans; } TVector operator*(const T& t) const { TVector ans(C); for (std::size_t i = 0; i < C; i++) { ans[i] = table[i] * t; } return ans; } TVector& operator=(const TVector& v) { assert(C == v.C); for (std::size_t i = 0; i < C; i++) { table[i] = v[i]; } return *this; } TVector& operator+=(const TVector& v) { assert(C == v.C); for (std::size_t i = 0; i < C; i++) { table[i] += v[i]; } return *this; } TVector& operator-=(const TVector& v) { assert(C == v.C); for (std::size_t i = 0; i < C; i++) { table[i] -= v[i]; } return *this; } TVector& operator*=(const T& t) { TVector ans(C); for (std::size_t i = 0; i < C; i++) { table[i] *= t; } return *this; } const std::size_t C; std::vector table; }; template TVector operator*(const T& t, const TVector& v) { return v * t; } template TVector operator*(const TVector& v, const Matrix& m) { assert(v.C == m.R); TVector ans(m.C); for (std::size_t i = 0; i < m.C; i++) { for (std::size_t j = 0; j < m.R; j++) { ans[i] += v[j] * m[j][i]; } } return ans; } template std::ostream& operator<<(std::ostream& os, const TVector& v) { os << "[ "; for (std::size_t i = 0; i < v.C; i++) { os << v[i] << " "; } return (os << "]\n"); } //!============================================!// //! 8888ba.88ba oo !// //! 88 '8b '8b !// //! 88 88 88 .d8888b. dP 88d888b. !// //! 88 88 88 88' '88 88 88' '88 !// //! 88 88 88 88. .88 88 88 88 !// //! dP dP dP '88888P8 dP dP dP !// //!============================================!// int main() { constexpr uint MOD = 998244353; using mint = ModInt; using Mat = Matrix; const int N = read(), K = read(); Mat m(K * K * K, K * K * K); auto encode = [&](const int i, const int j, const int k) { return i * K * K + j * K + k; }; for (int i = 0; i < K; i++) { for (int j = 0; j < K; j++) { for (int k = 0; k < K; k++) { m[encode((i + 1) % K, j, k)][encode(i, j, k)] += 1; m[encode(i, (i + j) % K, k)][encode(i, j, k)] += 1; m[encode(i, j, (j + k) % K)][encode(i, j, k)] += 1; } } } m ^= N; mint ans = 0; for (int i = 0; i < K * K * K; i++) { if (i % K == 0) { ans += m[i][0]; } } std::cout << ans << std::endl; return 0; }