#include /** * @title Modint * @docs mint.md */ template class ModInt{ public: constexpr static int32_t MOD = M; uint32_t val; constexpr ModInt(): val(0){} constexpr ModInt(int64_t n){ if(n >= M) val = n % M; else if(n < 0) val = n % M + M; else val = n; } constexpr auto& operator=(const ModInt &a){val = a.val; return *this;} constexpr auto& operator+=(const ModInt &a){ if(val + a.val >= M) val = (uint64_t)val + a.val - M; else val += a.val; return *this; } constexpr auto& operator-=(const ModInt &a){ if(val < a.val) val += M; val -= a.val; return *this; } constexpr auto& operator*=(const ModInt &a){ val = (uint64_t)val * a.val % M; return *this; } constexpr auto& operator/=(const ModInt &a){ val = (uint64_t)val * a.inv().val % M; return *this; } constexpr auto operator+(const ModInt &a) const {return ModInt(*this) += a;} constexpr auto operator-(const ModInt &a) const {return ModInt(*this) -= a;} constexpr auto operator*(const ModInt &a) const {return ModInt(*this) *= a;} constexpr auto operator/(const ModInt &a) const {return ModInt(*this) /= a;} constexpr bool operator==(const ModInt &a) const {return val == a.val;} constexpr bool operator!=(const ModInt &a) const {return val != a.val;} constexpr auto& operator++(){*this += 1; return *this;} constexpr auto& operator--(){*this -= 1; return *this;} constexpr auto operator++(int){auto t = *this; *this += 1; return t;} constexpr auto operator--(int){auto t = *this; *this -= 1; return t;} constexpr static ModInt power(int64_t n, int64_t p){ if(p < 0) return power(n, -p).inv(); int64_t ret = 1, e = n % M; for(; p; (e *= e) %= M, p >>= 1) if(p & 1) (ret *= e) %= M; return ret; } constexpr static ModInt inv(int64_t a){ int64_t b = M, u = 1, v = 0; while(b){ int64_t t = a / b; a -= t * b; std::swap(a,b); u -= t * v; std::swap(u,v); } u %= M; if(u < 0) u += M; return u; } constexpr static auto frac(int64_t a, int64_t b){return ModInt(a) / ModInt(b);} constexpr auto power(int64_t p) const {return power(val, p);} constexpr auto inv() const {return inv(val);} friend constexpr auto operator-(const ModInt &a){return ModInt(M-a.val);} friend constexpr auto operator+(int64_t a, const ModInt &b){return ModInt(a) + b;} friend constexpr auto operator-(int64_t a, const ModInt &b){return ModInt(a) - b;} friend constexpr auto operator*(int64_t a, const ModInt &b){return ModInt(a) * b;} friend constexpr auto operator/(int64_t a, const ModInt &b){return ModInt(a) / b;} friend std::istream& operator>>(std::istream &s, ModInt &a){s >> a.val; return s;} friend std::ostream& operator<<(std::ostream &s, const ModInt &a){s << a.val; return s;} template static auto div(){ static auto value = inv(N); return value; } explicit operator int32_t() const noexcept {return val;} explicit operator int64_t() const noexcept {return val;} }; /** * @title Factorial table * @docs factorial_table.md */ template class FactorialTable{ using value_type = T; std::vector f_table; std::vector if_table; public: FactorialTable(int N){ f_table.assign(N+1, 1); if_table.assign(N+1, 1); for(int i = 1; i <= N; ++i){ f_table[i] = f_table[i-1] * i; } if_table[N] = f_table[N].inv(); for(int i = N-1; i >= 0; --i){ if_table[i] = if_table[i+1] * (i+1); } } T factorial(int64_t i) const { assert(i < (int)f_table.size()); return f_table[i]; } T inv_factorial(int64_t i) const { assert(i < (int)if_table.size()); return if_table[i]; } T P(int64_t n, int64_t k) const { if(n < k or n < 0 or k < 0) return 0; return factorial(n) * inv_factorial(n-k); } T C(int64_t n, int64_t k) const { if(n < k or n < 0 or k < 0) return 0; return P(n,k) * inv_factorial(k); } T H(int64_t n, int64_t k) const { if(n == 0 and k == 0) return 1; return C(n+k-1, k); } }; namespace solver{ using mint = ModInt<998244353>; void solve(){ int64_t N, M; std::cin >> N >> M; auto ft = FactorialTable(M * 3); mint ans = 0; for(int i = 0; i <= M / N; ++i){ ans += ft.factorial(M - N * i + i) * ft.inv_factorial(M - N * i) * ft.inv_factorial(i); } std::cout << ans << "\n"; } } int main(){ solver::solve(); return 0; }