#pragma GCC optimize("Ofast") #pragma GCC optimize("unroll-loops") #pragma GCC push_options #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx") #include #include #include using namespace::std; __attribute__((constructor))void init(){cin.tie(0);ios::sync_with_stdio(false);cout< #include #include #include // #include // #include // namespace mp = boost::multiprecision; // typedef mp::number> cdouble; // typedef mp::cpp_int cint; templateusing pbds=__gnu_pbds::tree,__gnu_pbds::rb_tree_tag,__gnu_pbds::tree_order_statistics_node_update>; templateusing pbds_map=__gnu_pbds::tree,__gnu_pbds::rb_tree_tag,__gnu_pbds::tree_order_statistics_node_update>; templateusing hash_map=__gnu_pbds::gp_hash_table; templateusing pqueue =__gnu_pbds::priority_queue,__gnu_pbds::rc_binomial_heap_tag>; typedef long long lint; #define INF (1LL<<60) #define IINF (1<<30) #define LINF (9223372036854775807LL) #define EPS (1e-10) #define endl ('\n') //#define MOD 1000000007LL #define MOD 998244353LL //#define MOD 18446744069414584321ULL typedef vector vec; typedef vector> mat; typedef vector>> mat3; typedef vector svec; typedef vector> smat; templateinline void numout(T t){bool f=0;for(auto i:t){cout<<(f?" ":"")<inline void numout2(T t){for(auto i:t)numout(i);} templateinline void output(T t){bool f=0;for(auto i:t){cout<<(f?" ":"")<inline void output2(T t){for(auto i:t)output(i);} templateinline void _output(T t){bool f=0;for(lint i=0;iinline void _output2(T t){for(lint i=0;i=0;--i) #define rrepi(i,a,b) for(lint i=lint(b)-1;i>=lint(a);--i) #define irep(i) for(lint i=0;;++i) #define all(n) begin(n),end(n) #define dist(a,b,c,d) sqrt(pow(a-c,2)+pow(b-d,2)) inline lint gcd(lint A,lint B){return B?gcd(B,A%B):A;} inline lint lcm(lint A,lint B){return A/gcd(A,B)*B;} // inline cint cgcd(cint A,cint B){return B?cgcd(B,A%B):A;} // inline cint clcm(cint A,cint B){return A/cgcd(A,B)*B;} bool chmin(auto& s,const auto& t){bool res=s>t;s=min(s,t);return res;} bool chmax(auto& s,const auto& t){bool res=s dx={1,0,-1,0,1,1,-1,-1}; const vector dy={0,1,0,-1,1,-1,1,-1}; #define SUM(v) accumulate(all(v),0LL) auto call=[](auto f,auto... args){return f(f,args...);}; templateauto make_vector(T x,int arg,Args ...args){if constexpr(sizeof...(args)==0)return vector(arg,x);else return vector(arg,make_vector(x,args...));} template struct FPS_BASE:vector{ using vector::vector; using P=FPS_BASE; F fft; FPS_BASE(){} inline P operator +(T x)noexcept{return P(*this)+=x;} inline P operator -(T x)noexcept{return P(*this)-=x;} inline P operator *(T x)noexcept{return P(*this)*=x;} inline P operator /(T x)noexcept{return P(*this)/=x;} inline P operator <<(int x)noexcept{return P(*this)<<=x;} inline P operator >>(int x)noexcept{return P(*this)>>=x;} inline P operator +(const P& x)noexcept{return P(*this)+=x;} inline P operator -(const P& x)noexcept{return P(*this)-=x;} inline P operator -()noexcept{return P(1,T(0))-=P(*this);} inline P operator *(const P& x)noexcept{return this->operator*=(x);} inline P operator /(const P& x)noexcept{return P(*this)/=x;} inline P operator %(const P& x)noexcept{return P(*this)%=x;} P &operator +=(T x){ if(this->size()==0)this->resize(1,T(0)); (*this)[0]+=x; return (*this); } P &operator -=(T x){ if(this->size()==0)this->resize(1,T(0)); (*this)[0]-=x; return (*this); } P &operator *=(T x){ for(int i=0;i<(int)this->size();++i){ (*this)[i]*=x; } return (*this); } P &operator /=(T x){ return (*this)*=(T(1)/x); } P &operator <<=(int x){ P ret(x,T(0)); ret.insert(ret.end(),begin(*this),end(*this)); return (*this)=ret; } P &operator >>=(int x){ P ret; ret.insert(ret.end(),begin(*this)+x,end(*this)); return (*this)=ret; } P &operator +=(const P& x){ if(this->size()resize(x.size(),T(0)); for(int i=0;i<(int)x.size();++i){ (*this)[i]+=x[i]; } return (*this); } P &operator -=(const P& x){ if(this->size()resize(x.size(),T(0)); for(int i=0;i<(int)x.size();++i){ (*this)[i]-=x[i]; } return (*this); } P &operator *=(const P& x){ return (*this)=F()(*this,x); } P &operator /=(P x){ if(this->size()clear(); return (*this); } const int n=this->size()-x.size()+1; return (*this) = (rev().pre(n)*x.rev().inv(n)).pre(n).rev(n); } P &operator %=(const P& x){ return ((*this)-=*this/x*x); } inline P& shrink(){while((*this).back()==0)(*this).pop_back();return (*this);} inline P pre(int sz)const{ return P(begin(*this),begin(*this)+min((int)this->size(),sz)); } P rev(int deg=-1){ P ret(*this); if(deg!=-1)ret.resize(deg,T(0)); reverse(begin(ret),end(ret)); return ret; } P inv(int deg=-1){ assert((*this)[0]!=T(0)); const int n=deg==-1?this->size():deg; P ret({T(1)/(*this)[0]}); for(int i=1;isize(),x.size()));++i){ ret[i]*=x[i]; } return ret; } P diff(){ P ret(*this); for(int i=0;i<(int)ret.size();i++){ ret[i]*=i; } return ret>>1; } P integral(){ P ret(*this); for(int i=0;i<(int)ret.size();i++){ ret[i]/=i+1; } return ret<<1; } P log(int deg=-1){ assert((*this)[0]==T(1)); const int n=deg==-1?this->size():deg; return (diff()*inv(n)).pre(n-1).integral(); } P exp(int deg=-1){ assert((*this)[0]==T(0)); const int n=deg==-1?this->size():deg; P ret({T(1)}); for(int i=1;isize():deg; long long i=0; P ret(*this); while(i!=(int)this->size()&&ret[i]==0)i++; if(i==(int)this->size())return P(n,0); if(i*c>=n)return P(n,0); T k=ret[i]; return ((((ret>>i)/k).log()*c).exp()*(k.pow(c))<<(i*c)).pre(n); } P sqrt(int deg=-1){ const int n=deg==-1?this->size():deg; if((*this)[0]==T(0)) { for(int i=1;i<(int)this->size();i++) { if((*this)[i]!=T(0)) { if(i&1)return{}; if(n-i/2<=0)break; auto ret=(*this>>i).sqrt(n-i/2)<<(i/2); if((int)ret.size()size(); P f(*this),g(n,0); for(int i=0;i>=n-1; for(int i=0;isize()-1;i>=0;--i){ res*=x; res+=(*this)[i]; } return res; } vector multipoint_eval(const vector&x){ const int n=x.size(); P* v=new P[2*n-1]; for(int i=0;i=0;i--){v[i]=v[i*2+1]*v[i*2+2];} v[0]=P(*this)%v[0];v[0].shrink(); for(int i=1;ires(n); for(int i=0;i struct _FPS9{ auto operator()(auto s,auto t)->decltype(s){ auto ntt=[](auto v,const int& h,const bool& inv){ const int n=v.size(); assert(Mint::get_mod()>=3&&Mint::get_mod()%2==1); decltype(v) tmp(n,Mint()); Mint root=inv?Mint(Mint::root()).inv():Mint::root(); for(int b=n>>1;b>=1;b>>=1,v.swap(tmp)){ Mint w=root.pow((Mint::get_mod()-1)/(n/b)),p=1; for(int i=0;iusing fps=FPS_BASE>; class mint { using u64 = std::uint_fast64_t; public: u64 a; constexpr mint(const long long x = 0)noexcept:a(x>=0?x%get_mod():get_mod()-(-x)%get_mod()){} constexpr u64 &value()noexcept{return a;} constexpr const u64 &value() const noexcept {return a;} constexpr mint operator+(const mint rhs)const noexcept{return mint(*this) += rhs;} constexpr mint operator-(const mint rhs)const noexcept{return mint(*this)-=rhs;} constexpr mint operator*(const mint rhs) const noexcept {return mint(*this) *= rhs;} constexpr mint operator/(const mint rhs) const noexcept {return mint(*this) /= rhs;} constexpr mint &operator+=(const mint rhs) noexcept { a += rhs.a; if (a >= get_mod())a -= get_mod(); return *this; } constexpr mint &operator-=(const mint rhs) noexcept { if (a= get_mod())a -= get_mod(); return *this; } constexpr mint operator--(int n) noexcept { if (a<1)a += get_mod(); a -= 1; return *this; } constexpr mint &operator/=(mint rhs) noexcept { u64 exp=get_mod()-2; while (exp) { if (exp % 2) { *this *= rhs; } rhs *= rhs; exp /= 2; } return *this; } constexpr bool operator==(mint x) noexcept { return a==x.a; } constexpr bool operator!=(mint x) noexcept { return a!=x.a; } constexpr bool operator<(mint x) noexcept { return a(mint x) noexcept { return a>x.a; } constexpr bool operator<=(mint x) noexcept { return a<=x.a; } constexpr bool operator>=(mint x) noexcept { return a>=x.a; } constexpr static int root(){ mint root = 2; while(root.pow((get_mod()-1)>>1).a==1)root++; return root.a; } constexpr mint pow(long long n){ long long x=a; mint ret = 1; while(n>0) { if(n&1)(ret*=x); (x*=x)%=get_mod(); n>>=1; } return ret; } constexpr mint inv(){ return pow(get_mod()-2); } static vector fac,ifac; static bool init; constexpr static int mx=10000001; void build(){ init=0; fac.resize(mx); ifac.resize(mx); fac[0]=1,ifac[0]=1; for(int i=1;i=0;i--)ifac[i]=ifac[i+1]*(i+1); } mint comb(lint b){ if(init)build(); if(a==0&&b==0)return 1; if((lint)a>(istream& lhs,mint& rhs) noexcept { lhs >> rhs.a; return lhs; } constexpr static u64 get_mod(){return MOD;} }; vector mint::fac; vector mint::ifac; bool mint::init=1; int main(){ lint n,k; cin>>n>>k; mint ans=mint(k).pow(n)/2; rep(i,k+1){ ans-=mint(k).comb(i)*mint(-2).pow(i)*mint(k-i).pow(n)/2; } cout<