#line 1 "D_modint.cpp" #include ; #line 1 "/home/ecasdqina/cpcpp/libs/library_cpp/math/modint.hpp" #include namespace cplib { template class modint { using u32 = std::uint_fast32_t; using u64 = std::uint_fast64_t; using i32 = std::int_fast32_t; using i64 = std::int_fast64_t; inline u64 apply(i64 x) { return (x < 0 ? x + Modulus : x); }; public: u64 a; static constexpr u64 mod = Modulus; constexpr modint(const i64& x = 0) noexcept: a(apply(x % (i64)Modulus)) {} 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 u64& k) const noexcept { return modint(*this) ^= k; } constexpr modint operator^(const modint& k) const noexcept { return modint(*this) ^= k.value(); } constexpr modint operator-() const noexcept { return modint(Modulus - a); } constexpr modint operator++() noexcept { return (*this) = modint(*this) + 1; } constexpr modint operator--() noexcept { return (*this) = modint(*this) - 1; } const bool operator==(const modint& rhs) const noexcept { return a == rhs.a; }; const bool operator!=(const modint& rhs) const noexcept { return a != rhs.a; }; const bool operator<=(const modint& rhs) const noexcept { return a <= rhs.a; }; const bool operator>=(const modint& rhs) const noexcept { return a >= rhs.a; }; const bool operator<(const modint& rhs) const noexcept { return a < rhs.a; }; const bool operator>(const modint& rhs) const noexcept { return a > rhs.a; }; 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 = Modulus - 2; while (exp) { if (exp % 2) (*this) *= rhs; rhs *= rhs; exp /= 2; } return *this; } constexpr modint& operator^=(u64 k) noexcept { auto b = modint(1); while(k) { if(k & 1) b = b * (*this); (*this) *= (*this); k >>= 1; } return (*this) = b; } constexpr modint& operator=(const modint& rhs) noexcept { a = rhs.a; return (*this); } const modint inverse() const { return modint(1) / *this; } const modint power(i64 k) const { if(k < 0) return modint(*this).inverse() ^ (-k); return modint(*this) ^ k; } explicit operator bool() const { return a; } explicit operator u64() const { return a; } constexpr u64& value() noexcept { return a; } constexpr const u64& value() const noexcept { return a; } friend std::ostream& operator<<(std::ostream& os, const modint& p) { return os << p.a; } friend std::istream& operator>>(std::istream& is, modint& p) { u64 t; is >> t; p = modint(t); return is; } }; } #line 4 "D_modint.cpp" using mint = cplib::modint<998244353>; int main() { int n, k; scanf("%d%d", &n, &k); // 線形篩 std::vector primes, minp(k + 1, -1); for(int i = 2; i < minp.size(); i++) { if(minp[i] == -1) { minp[i] = i; primes.push_back(i); } for(int p: primes) { if(p * i >= minp.size() or p > minp[i]) break; minp[p * i] = p; } } // べき乗列挙 std::vector powers(k + 1); powers[1] = 1; for(int p: primes) powers[p] = mint(p).power(n - 1); for(int i = 4; i < powers.size(); i++) if(minp[i] != i) { powers[i] = powers[i / minp[i]] * powers[minp[i]]; } auto f = [&](int x) -> mint { const mint A = powers[k] * k; const mint B = powers[k - x] * x * n; const mint C = powers[k - x] * (k - x); return A - B - C; }; mint ans = 0; for(int i = 1; i <= k; i++) { mint count = f(i) - f(i - 1); ans += count * (k - i + 1); } printf("%lld\n", ans.value()); }