//#define NDEBUG #include #include #include namespace n91 { using i8 = std::int_fast8_t; using i32 = std::int_fast32_t; using i64 = std::int_fast64_t; using u8 = std::uint_fast8_t; using u32 = std::uint_fast32_t; using u64 = std::uint_fast64_t; using isize = std::ptrdiff_t; using usize = std::size_t; constexpr usize operator"" _z(unsigned long long x) { return static_cast(x); } class rep { const usize f, l; public: class itr { friend rep; usize i; constexpr itr(const usize x) noexcept : i(x) {} public: void operator++() noexcept { ++i; } constexpr usize operator*() const noexcept { return i; } constexpr bool operator!=(const itr x) const noexcept { return i != x.i; } }; constexpr rep(const usize first, const usize last) noexcept : f(first), l(last) {} constexpr itr begin() const noexcept { return itr(f); } constexpr itr end() const noexcept { return itr(l); } }; class revrep { const usize f, l; public: class itr { friend revrep; usize i; constexpr itr(usize x) noexcept : i(x) {} public: void operator++() noexcept { --i; } constexpr usize operator*() const noexcept { return i; } constexpr bool operator!=(const itr x) const noexcept { return i != x.i; } }; constexpr revrep(usize first, usize last) noexcept : f(--first), l(--last) {} constexpr itr begin() const noexcept { return itr(l); } constexpr itr end() const noexcept { return itr(f); } }; template using vec_alias = std::vector; template auto md_vec(const usize n, const T &value) { return std::vector(n, value); } template auto md_vec(const usize n, Args... args) { return std::vector(n, md_vec(args...)); } template constexpr T difference(const T &a, const T &b) { return a < b ? b - a : a - b; } } // namespace n91 #include namespace n91 { constexpr std::uint_fast64_t totient(std::uint_fast64_t x) noexcept { using u64 = std::uint_fast64_t; u64 ret = x; for (u64 i = static_cast(2); i * i <= x; ++i) { if (x % i == static_cast(0)) { ret -= ret / i; x /= i; while (x % i == static_cast(0)) { x /= i; } } } if (x != static_cast(1)) { ret -= ret / x; } return ret; } template (1)> class modint { using u64 = std::uint_fast64_t; static_assert(Modulus < static_cast(1) << static_cast(32), "Modulus must be less than 2**32"); u64 a; constexpr modint &negate() noexcept { if (a != static_cast(0)) { a = Modulus - a; } return *this; } public: constexpr modint(const u64 x = static_cast(0)) noexcept : a(x % Modulus) {} constexpr u64 &value() noexcept { return a; } constexpr u64 value() const noexcept { return a; } constexpr modint operator+() const noexcept { return modint(*this); } constexpr modint operator-() const noexcept { return modint(*this).negate(); } constexpr modint operator+(const modint rhs) const noexcept { return modint(*this) += rhs; } constexpr modint operator-(const modint rhs) const noexcept { return modint(*this) -= rhs; } constexpr modint operator*(const modint rhs) const noexcept { return modint(*this) *= rhs; } constexpr modint operator/(const modint rhs) const noexcept { return modint(*this) /= rhs; } constexpr modint &operator+=(const modint rhs) noexcept { a += rhs.a; if (a >= Modulus) { a -= Modulus; } return *this; } constexpr modint &operator-=(const modint rhs) noexcept { if (a < rhs.a) { a += Modulus; } a -= rhs.a; return *this; } constexpr modint &operator*=(const modint rhs) noexcept { a = a * rhs.a % Modulus; return *this; } constexpr modint &operator/=(modint rhs) noexcept { u64 exp = InverseExp; while (exp) { if (exp % static_cast(2) != static_cast(0)) { *this *= rhs; } rhs *= rhs; exp /= static_cast(2); } return *this; } constexpr bool operator==(const modint rhs) const noexcept { return a == rhs.a; } constexpr bool operator!=(const modint rhs) const noexcept { return a != rhs.a; } }; } // namespace n91 #include #include #include #include #include template class array_matrix : public std::array, N> { public: array_matrix() { std::for_each(this->begin(), this->end(), [](auto &row) { std::fill(row.begin(), row.end(), static_cast(0)); }); } array_matrix(std::initializer_list> il) { assert(il.size() == N); auto ar_itr = this->begin(); const auto ar_end = this->end(); auto il_itr = il.begin(); while (ar_itr != ar_end) { assert(il_itr->size() == M); std::copy(il_itr->begin(), il_itr->end(), ar_itr->begin()); ++ar_itr; ++il_itr; } } }; template array_matrix operator*(const array_matrix &lhs, const array_matrix &rhs) { array_matrix ret = {}; for (std::size_t i = static_cast(0); i != N; ++i) { for (std::size_t j = static_cast(0); j != M; ++j) { for (std::size_t k = static_cast(0); k != L; ++k) { ret[i][k] += lhs[i][j] * rhs[j][k]; } } } return ret; } template array_matrix identity() { array_matrix ret; for (std::size_t i = static_cast(0); i != N; ++i) { ret[i][i] = static_cast(1); } return ret; } #include #include namespace n91 { template > constexpr T power(T base, U exp, const Operate &oper = Operate(), T iden = static_cast(1)) { while (exp != static_cast(0)) { if (exp % static_cast(2) != static_cast(0)) { iden = oper(iden, base); } exp /= static_cast(2); base = oper(base, base); } return iden; } } // namespace n91 #include #include #include namespace n91 { void main_() { u64 n; usize k; std::cin >> n >> k; using mint = modint<998244353>; array_matrix trans; const auto get = [&k](const usize i, const usize j, const usize s) { return k * k * i + k * j + s; }; for (const auto i : rep(0_z, k)) { for (const auto j : rep(0_z, k)) { for (const auto s : rep(0_z, k)) { trans[get(i, j, s)][get((i + 1_z) % k, j, s)] += static_cast(1); trans[get(i, j, s)][get(i, (j + i) % k, s)] += static_cast(1); trans[get(i, j, s)][get(i, j, (s + j) % k)] += static_cast(1); } } } array_matrix vec; vec[0_z][0_z] = static_cast(1); auto ret = vec * power(trans, n, std::multiplies<>(), identity()); mint ans = static_cast(0); for (const auto i : rep(0, k)) { for (const auto j : rep(0, k)) { ans += ret[0_z][get(i, j, 0_z)]; } } std::cout << ans.value() << std::endl; } } // namespace n91 int main() { n91::main_(); return 0; }