#include #include #include #include #include #include template inline bool chmin(T &lhs, const U &rhs) { if (lhs > rhs) { lhs = rhs; return true; } return false; } template inline bool chmax(T &lhs, const U &rhs) { if (lhs < rhs) { lhs = rhs; return true; } return false; } struct range { using itr = int64_t; struct iterator { itr i; constexpr iterator(itr i_) noexcept : i(i_) { } constexpr void operator ++ () noexcept { ++i; } constexpr itr operator * () const noexcept { return i; } constexpr bool operator != (iterator x) const noexcept { return i != x.i; } }; const iterator l, r; constexpr range(itr l_, itr r_) noexcept : l(l_), r(std::max(l_, r_)) { } constexpr iterator begin() const noexcept { return l; } constexpr iterator end() const noexcept { return r; } }; struct revrange { using itr = int64_t; struct iterator { itr i; constexpr iterator(itr i_) noexcept : i(i_) { } constexpr void operator ++ () noexcept { --i; } constexpr itr operator * () const noexcept { return i; } constexpr bool operator != (iterator x) const noexcept { return i != x.i; } }; const iterator l, r; constexpr revrange(itr l_, itr r_) noexcept : l(l_ - 1), r(std::max(l_, r_) - 1) { } constexpr iterator begin() const noexcept { return r; } constexpr iterator end() const noexcept { return l; } }; using i32 = int32_t; using i64 = int64_t; using u32 = uint32_t; using u64 = uint64_t; constexpr i32 inf32 = (i32(1) << 30) - 1; constexpr i64 inf64 = (i64(1) << 62) - 1; template class modular { public: using value_type = uint32_t; using max_type = uint64_t; static constexpr value_type mod = Modulus; static constexpr value_type get_mod() { return mod; } static_assert(mod >= 2, "invalid mod :: smaller than 2"); static_assert(mod < (value_type(1) << 31), "invalid mod :: over 2^31"); template static constexpr value_type normalize(T value_) { if (value_ < 0) { value_ = -value_; value_ %= mod; if (value_ == 0) return 0; return mod - value_; } return value_ % mod; } private: value_type value; public: constexpr modular(): value(0) { } template explicit constexpr modular(T value_): value(normalize(value_)) { } template explicit constexpr operator T() { return static_cast(value); } constexpr value_type get() const { return value; } constexpr modular operator - () const { return modular(mod - value); } constexpr modular operator ~ () const { return inverse(); } constexpr value_type &extract() { return value; } constexpr modular inverse() const { return power(mod - 2); } constexpr modular power(max_type exp) const { modular res(1), mult(*this); while (exp > 0) { if (exp & 1) res *= mult; mult *= mult; exp >>= 1; } return res; } constexpr modular operator + (const modular &rhs) const { return modular(*this) += rhs; } constexpr modular& operator += (const modular &rhs) { if ((value += rhs.value) >= mod) value -= mod; return *this; } constexpr modular operator - (const modular &rhs) const { return modular(*this) -= rhs; } constexpr modular& operator -= (const modular &rhs) { if ((value += mod - rhs.value) >= mod) value -= mod; return *this; } constexpr modular operator * (const modular &rhs) const { return modular(*this) *= rhs; } constexpr modular& operator *= (const modular &rhs) { value = (max_type) value * rhs.value % mod; return *this; } constexpr modular operator / (const modular &rhs) const { return modular(*this) /= rhs; } constexpr modular& operator /= (const modular &rhs) { return (*this) *= rhs.inverse(); } constexpr bool zero() const { return value == 0; } constexpr bool operator == (const modular &rhs) const { return value == rhs.value; } constexpr bool operator != (const modular &rhs) const { return value != rhs.value; } friend std::ostream& operator << (std::ostream &stream, const modular &rhs) { return stream << rhs.value; } }; template class factorials { public: using value_type = T; static constexpr std::size_t size = N; public: std::array fact{}; std::array fact_inv{}; factorials() { fact.front() = value_type(1); for (std::size_t i = 1; i <= size; ++i) { fact[i] = fact[i - 1] * value_type(i); } fact_inv.back() = ~fact.back(); for (std::size_t i = size; i > 0; --i) { fact_inv[i - 1] = fact_inv[i] * value_type(i); } } value_type operator () (std::size_t n, std::size_t r) const { return fact[n] * fact_inv[n - r] * fact_inv[r]; } }; using m32 = modular<998244353>; factorials fact; int main() { i32 N, K; std::cin >> N >> K; m32 ans = m32(K).power(N); for (auto i: range(0, K + 1)) { ans += m32(2).power(K - i) * m32(i).power(N) * fact(K, i) * m32((i & 1 ? 1 : -1) * (K & 1 ? -1 : 1)); } std::cout << ans / m32(2) << '\n'; return 0; }