#pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include #include // cout, endl, cin #include // string, to_string, stoi #include // vector #include // min, max, swap, sort, reverse, lower_bound, upper_bound #include // pair, make_pair #include // tuple, make_tuple #include // int64_t, int*_t #include // printf #include // map #include // queue, priority_queue #include // set #include // stack #include // deque #include // unordered_map #include // unordered_set #include // bitset #include // isupper, islower, isdigit, toupper, tolower #include #include #include using namespace std; using namespace atcoder; #define rep(i, n) for (int i = 0; i < (int)(n); i++) #define repi(i, a, b) for (int i = (int)(a); i < (int)(b); i++) typedef long long ll; typedef unsigned long long ull; const ll inf=1e18; using graph = vector > ; using P= pair; using vi=vector; using vvi=vector; using vll=vector; using vvll=vector; using vp=vector

; using vpp=vector; using vd=vector; using vvd =vector; //string T="ABCDEFGHIJKLMNOPQRSTUVWXYZ"; //string S="abcdefghijklmnopqrstuvwxyz"; //g++ main.cpp -std=c++17 -I . //cout < bool chmin(T& a, T b) { if (a > b) { a = b; return true; } else return false; } template bool chmax(T& a, T b) { if (a < b) { a = b; return true; } else return false; } // https://youtu.be/L8grWxBlIZ4?t=9858 // https://youtu.be/ERZuLAxZffQ?t=4807 : optimize // https://youtu.be/8uowVvQ_-Mo?t=1329 : division ll mod =998244353; struct mint { ll x; // typedef long long ll; mint(ll x=0):x((x%mod+mod)%mod){} mint operator-() const { return mint(-x);} mint& operator+=(const mint a) { if ((x += a.x) >= mod) x -= mod; return *this; } mint& operator-=(const mint a) { if ((x += mod-a.x) >= mod) x -= mod; return *this; } mint& operator*=(const mint a) { (x *= a.x) %= mod; return *this;} mint operator+(const mint a) const { return mint(*this) += a;} mint operator-(const mint a) const { return mint(*this) -= a;} mint operator*(const mint a) const { return mint(*this) *= a;} mint pow(ll t) const { if (!t) return 1; mint a = pow(t>>1); a *= a; if (t&1) a *= *this; return a; } // for prime mod mint inv() const { return pow(mod-2);} mint& operator/=(const mint a) { return *this *= a.inv();} mint operator/(const mint a) const { return mint(*this) /= a;} }; istream& operator>>(istream& is, const mint& a) { return is >> a.x;} ostream& operator<<(ostream& os, const mint& a) { return os << a.x;} // combination mod prime // https://www.youtube.com/watch?v=8uowVvQ_-Mo&feature=youtu.be&t=1619 struct combination { vector fact, ifact; combination(int n):fact(n+1),ifact(n+1) { //assert(n < mod); fact[0] = 1; for (int i = 1; i <= n; ++i) fact[i] = fact[i-1]*i; ifact[n] = fact[n].inv(); for (int i = n; i >= 1; --i) ifact[i-1] = ifact[i]*i; } mint operator()(int n, int k) { if (k < 0 || k > n) return 0; return fact[n]*ifact[k]*ifact[n-k]; } mint p(int n, int k) { return fact[n]*ifact[n-k]; } } c(500000); using vm=vector ; using vvm=vector ; ll sqrt_(ll x) { ll l = 0, r = ll(3e9)+1; while (l+1=0 && y>=0 && x struct Matrix { int h, w; vector > d; Matrix() {} Matrix(int h, int w, T val=0): h(h), w(w), d(h, vector(w,val)) {} Matrix& unit() { //assert(h == w); rep(i,h) d[i][i] = 1; return *this; } const vector& operator[](int i) const { return d[i];} vector& operator[](int i) { return d[i];} Matrix operator*(const Matrix& a) const { //assert(w == a.h); Matrix r(h, a.w); rep(i,h)rep(k,w)rep(j,a.w) { r[i][j] += d[i][k]*a[k][j]; } return r; } Matrix pow(ll t) const { // assert(h == w); if (!t) return Matrix(h,h).unit(); if (t == 1) return *this; Matrix r = pow(t>>1); r = r*r; if (t&1) r = r*(*this); return r; } }; using ve=vector; using vve=vector; //g++ main.cpp -std=c++17 -I . int main(){cin.tie(0);ios::sync_with_stdio(false); int n,m; cin >> n >> m; vector a(n+1); vector b(1); b[0]=1; vm pow2(n+1,1); vm kai(n+1,1); vm kaiinv(n+1,1); for(int i=1; i<=n; i++)pow2[i]=pow2[i-1]*2; for(int i=1; i<=n; i++)kai[i]=kai[i-1]*i; for(int i=1; i<=n; i++)kaiinv[i]=kai[i].inv(); for(int i=0; i<=n; i++){ a[i]=((pow2[i]-1)*kaiinv[i]).x; } vvm pow3(n+1,vm(n+1,1)); for(int i=1; i<=n; i++){ int x=m+1-i; if(x<=0)break; for(int j=1; j<=n; j++)pow3[i][j]=pow3[i][j-1]*x; } mint ans=0; for(int i=1; i<=n; i++){ if(i-1>m)break; auto x=convolution(a,b); int si=x.size(); b.clear(); b.resize(min(si,n+1)); for(int i=0; in)break; b[i]=x[i]; } for(int j=1; j<=n; j++){ if(si<=j)break; mint now=pow2[n-j]; // if(n-j>0)now*=pow_pow(m+1-i,n-j,mod); if(n-j>0)now*=pow3[i][n-j]; now*=(kai[n]*b[j]); now*=kaiinv[n-j]; ans+=now; } } cout << ans << endl; }