#include #include #include #include #include #include #include #include #include #include #include #include #include #define debug_value(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << #x << "=" << x << endl; #define debug(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << x << endl; template inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; } template inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; } using namespace std; typedef long long ll; template vector> vec2d(int n, int m, T v){ return vector>(n, vector(m, v)); } template vector>> vec3d(int n, int m, int k, T v){ return vector>>(n, vector>(m, vector(k, v))); } template void print_vector(vector v, char delimiter=' '){ if(v.empty()) { cout << endl; return; } for(int i = 0; i+1 < v.size(); i++) cout << v[i] << delimiter; cout << v.back() << endl; } const ll MOD = 998244353; class ModInt{ public: ll v; ModInt(ll _v = 0){ if(_v < 0) _v = (_v%MOD)+MOD; if(_v >= MOD) _v %= MOD; v = _v; } ModInt operator+(ll n){ return ModInt((v+n)%MOD); } ModInt operator-(ll n){ return ModInt((v-n+MOD)%MOD); } ModInt operator*(ll n){ if(n >= MOD) n %= MOD; return ModInt((v*n)%MOD); } ModInt operator/(ll n){ return ModInt((ModInt(n).inv()*v).v%MOD); } ModInt &operator+=(ll n){ v = (v+n)%MOD; return *this; } ModInt &operator-=(ll n){ v = (v-n+MOD)%MOD; return *this; } ModInt &operator*=(ll n){ v = (v*n+MOD)%MOD; return *this; } ModInt operator+(ModInt n){ return ModInt((v+n.v)%MOD); } ModInt operator-(ModInt n){ return ModInt((v-n.v+MOD)%MOD); } ModInt operator*(ModInt n){ return ModInt((v*n.v)%MOD); } ModInt operator/(ModInt n){ return ModInt((n.inv()*v).v%MOD); } ModInt &operator+=(ModInt n){ v = (v+n.v)%MOD; return *this; } ModInt &operator-=(ModInt n){ v = (v-n.v+MOD)%MOD; return *this; } ModInt &operator*=(ModInt n){ v = (v*n.v)%MOD; return *this; } bool operator==(ModInt n){ return v == n.v; } bool operator!=(ModInt n){ return v != n.v; } ModInt &operator=(ll n){ v = n%MOD; return *this; } ModInt inv(){ if(v == 1) return ModInt(1); else return ModInt(MOD-ModInt(MOD%v).inv().v*(MOD/v)%MOD); } }; ostream& operator<<(ostream& os, const ModInt& m){ os << m.v; return os; } istream & operator >> (istream &in, ModInt &m){ in >> m.v; return in; } ModInt pow(ModInt a, ll n) { assert(n >= 0); ModInt ans = 1; while (n > 0) { if (n&1) ans = ans*a; a = a*a; n >>= 1; } return ans; } using mint = ModInt; #define N_MAX 200002 ModInt inv[N_MAX],fac[N_MAX],finv[N_MAX]; void init(){ fac[0]=1;fac[1]=1; finv[0]=1;finv[1]=1; inv[1]=1; for(int i=2;i class Cumsum{ public: Cumsum(vector v): v(v){ n = v.size(); v_cumsum = vector(n+1, T(0)); for(int i = 0; i < n; i++) v_cumsum[i+1] = v_cumsum[i]+v[i]; } /** * v[l] + ... + v[r-1] */ T sum(int l, int r){ if(r <= l) return T(0); if(r > n) r = n; if(l < 0) l = 0; return v_cumsum[r]-v_cumsum[l]; } private: int n; vector v; vector v_cumsum; }; int main(){ ios::sync_with_stdio(false); cin.tie(0); cout << setprecision(10) << fixed; init(); int n, k; cin >> n >> k; auto dp = vec2d(k+1, n+1, mint(0)); dp[0][0] = 1; for(int i = 1; i <= k; i++){ dp[i][0] = 1; auto cumsum = Cumsum(dp[i-1]); for(int j = 1; j <= n; j++){ dp[i][j] = cumsum.sum(0, j)*inv[j]; } } cout << dp[k][n] << endl; }