#include #include #include #include #include #include #include // modint構造体 template struct mod_Int{ int val; // 値本体 // コンストラクタ constexpr mod_Int():val(0){} constexpr mod_Int(const int& v):val(v % modulus){ if(val < 0) val += modulus; } constexpr mod_Int(int&& v):val(v % modulus){ if(val < 0) val += modulus; } constexpr mod_Int(const long long int& v):val(v % modulus){ if(val < 0) val += modulus; } constexpr mod_Int(long long int&& v):val(v % modulus){ if(val < 0) val += modulus; } constexpr mod_Int(const unsigned int& v):val(v % modulus){} constexpr mod_Int(unsigned int&& v):val(v % modulus){} constexpr mod_Int(const unsigned long long int& v):val(v % modulus){} constexpr mod_Int(unsigned long long int&& v):val(v % modulus){} constexpr mod_Int& operator += (const mod_Int& other) noexcept { val += other.val; if(val >= modulus) val -= modulus; return *this; } constexpr mod_Int& operator -= (const mod_Int& other) noexcept { val -= other.val; if(val < 0) val += modulus; return *this; } constexpr mod_Int& operator *= (const mod_Int& other) noexcept { val = static_cast(val) * other.val % modulus; return *this; } constexpr mod_Int& operator /= (const mod_Int& other) noexcept { val = static_cast(val) * other.inverse() % modulus; return *this; } constexpr bool operator == (const mod_Int& other) const noexcept { return val == other.val; } constexpr mod_Int operator +(const mod_Int& v) const noexcept{ return mod_Int(*this) += v; } constexpr mod_Int operator -(const mod_Int& v)const noexcept{ return mod_Int(*this) -= v; } constexpr mod_Int operator *(const mod_Int& v) const noexcept{ return mod_Int(*this) *= v; } constexpr mod_Int operator /(const mod_Int& v) const noexcept{ return mod_Int(*this) /= v; } constexpr mod_Int& operator ++(void) noexcept { if(++val == modulus) val = 0; return *this; } constexpr mod_Int& operator --(void) noexcept { if(val-- == 0) val = modulus - 1; return *this; } constexpr mod_Int operator -()const noexcept{ return mod_Int((val == 0 ? 0 : modulus - val)); } // aの逆元を求める関数 static constexpr int inverse(int a) noexcept { int b = modulus, u = 1, v = 0; while (b != 0) { const int t = a / b; a -= t * b; std::swap(a, b); u -= t * v; std::swap(u, v); } if(u < 0) u += modulus; return u; } constexpr int inverse(void) const noexcept { return inverse(val); } // a^nを返す関数 : nは負の数でも可 static constexpr int power(int a, long long int n){ long long res = 1, waiting = a; if(n < 0) waiting = inverse(a), n = -n; while(n != 0){ if(n % 2 != 0) res = res * waiting % modulus; waiting = waiting * waiting % modulus; n /= 2; } return res; } constexpr mod_Int power(long long int n) const noexcept { mod_Int res; res.val = power(val, n); return res; } friend std::ostream& operator << (std::ostream& os_arg, const mod_Int& mod_Int_arg){ os_arg << mod_Int_arg.val; return os_arg; } }; template struct Combination{ const int sz; std::vector> Power, Inv_Power, Inv; // コンストラクタ : n は想定される最大値 Combination(const int n):sz(n){ Power.resize(n + 1); Power[0].val = 1; mod_Int v = 1; for(int i = 1; i <= n; ++i, ++v) Power[i] = Power[i - 1] * v; Inv_Power.resize(n + 1); Inv_Power[n] = Power[n].inverse(); v = n; for(int i = n; i > 0; --i, --v) Inv_Power[i - 1] = Inv_Power[i] * v; Inv.resize(n + 1); Inv[0] = 0; for(int i = 1; i <= n; ++i) Inv[i] = Inv_Power[i] * Power[i - 1]; } // 組み合わせ nCk を求める関数 mod_Int combination(const int n, const int k) const { if(k < 0 or n < k) return mod_Int(); return Power[n] * Inv_Power[k] * Inv_Power[n - k]; } }; constexpr int mod = 998244353; using modint = mod_Int; int main(void){ std::cin.tie(nullptr); std::ios_base::sync_with_stdio(false); std::cout << std::fixed << std::setprecision(16); int n, m; std::cin >> n >> m; if(n == 1){ std::cout << "1\n"; return 0; } Combination C(20'000'000); modint res; for(int k = 0, r = m; r >= 0; ++k, r -= n) res += C.combination(r + k, k); std::cout << res << '\n'; return 0; }