Language: C++

#include <bits/stdc++.h>
using namespace std;

using ll=long long;
#define int ll

#define rng(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,b) rng(i,0,b)
#define gnr(i,a,b) for(int i=int(b)-1;i>=a;i--)
#define per(i,b) gnr(i,0,b)
#define pb push_back
#define eb emplace_back
#define a first
#define b second
#define bg begin()
#define ed end()
#define all(x) x.bg,x.ed
#ifdef LOCAL
#define dmp(x) cerr<<__LINE__<<" "<<#x<<" "<<x<<endl
#else
#define dmp(x) void(0)
#endif

template<class t,class u> void chmax(t&a,u b){if(a<b)a=b;}
template<class t,class u> void chmin(t&a,u b){if(b<a)a=b;}

template<class t> using vc=vector<t>;
template<class t> using vvc=vc<vc<t>>;

using pi=pair<int,int>;
using vi=vc<int>;

template<class t,class u>
ostream& operator<<(ostream& os,const pair<t,u>& p){
	return os<<"{"<<p.a<<","<<p.b<<"}";
}

template<class t> ostream& operator<<(ostream& os,const vc<t>& v){
	os<<"{";
	for(auto e:v)os<<e<<",";
	return os<<"}";
}

#define mp make_pair
#define mt make_tuple

using uint=unsigned;
using ull=unsigned long long;

template<int i,class T>
void print_tuple(ostream&,const T&){
}

template<int i,class T,class H,class ...Args>
void print_tuple(ostream&os,const T&t){
	if(i)os<<",";
	os<<get<i>(t);
	print_tuple<i+1,T,Args...>(os,t);
}

template<class ...Args>
ostream& operator<<(ostream&os,const tuple<Args...>&t){
	os<<"{";
	print_tuple<0,tuple<Args...>,Args...>(os,t);
	return os<<"}";
}

void print(ll x,int suc=1){
	cout<<x;
	if(suc==1)
		cout<<endl;
	if(suc==2)
		cout<<" ";
}

ll read(){
	ll i;
	cin>>i;
	return i;
}

vi readvi(int n,int off=0){
	vi v(n);
	rep(i,n)v[i]=read()+off;
	return v;
}

template<class T>
void print(const vector<T>&v,int suc=1){
	rep(i,v.size())
		print(v[i],i==int(v.size())-1?suc:2);
}

string readString(){
	string s;
	cin>>s;
	return s;
}

template<class T>
T sq(const T& t){
	return t*t;
}

//#define CAPITAL
void yes(bool ex=true){
	#ifdef CAPITAL
	cout<<"YES"<<endl;
	#else
	cout<<"Yes"<<endl;
	#endif
	if(ex)exit(0);
}
void no(bool ex=true){
	#ifdef CAPITAL
	cout<<"NO"<<endl;
	#else
	cout<<"No"<<endl;
	#endif
	if(ex)exit(0);
}

constexpr ll ten(int n){
	return n==0?1:ten(n-1)*10;
}

const ll infLL=LLONG_MAX/3;

#ifdef int
const int inf=infLL;
#else
const int inf=INT_MAX/2-100;
#endif

int topbit(signed t){
	return t==0?-1:31-__builtin_clz(t);
}
int topbit(ll t){
	return t==0?-1:63-__builtin_clzll(t);
}
int popcount(signed t){
	return __builtin_popcount(t);
}
int popcount(ll t){
	return __builtin_popcountll(t);
}
bool ispow2(int i){
	return i&&(i&-i)==i;
}

bool inc(int a,int b,int c){
	return a<=b&&b<=c;
}

template<class t> void mkuni(vc<t>&v){
	sort(all(v));
	v.erase(unique(all(v)),v.ed);
}

ll rand_int(ll l, ll r) { //[l, r]
    static random_device rd;
    static mt19937 gen(rd());
    return uniform_int_distribution<ll>(l, r)(gen);
}

using uint=unsigned;
using ull=unsigned long long;

const uint mod=998244353;
//const uint mod=1000000007;
struct ModInt{
	uint a;
    ModInt(ll x=0):a((x%mod+mod)%mod){}

	ModInt& operator+=(const ModInt &x){
		a+=x.a;
		if(a>=mod)a-=mod;
		return *this;
	}
	ModInt& operator-=(const ModInt &x){
		a+=mod-x.a;
        if(a>=mod)a-=mod;
		return *this;
	}
	ModInt& operator*=(const ModInt &x){
		a=ull(a)*x.a%mod;
		return *this;
	}
	ModInt& operator/=(const ModInt &x){
		*this*=x.inv();
		return *this;
	}

	ModInt operator+(const ModInt &x)const{return ModInt(*this)+=x;}
	ModInt operator-(const ModInt &x)const{return ModInt(*this)-=x;}
	ModInt operator*(const ModInt &x)const{return ModInt(*this)*=x;}
	ModInt operator/(const ModInt &x)const{return ModInt(*this)/=x;}
	bool operator==(const ModInt &x)const{return a==x.a;}
	bool operator!=(const ModInt &x)const{return a!=x.a;}

	ModInt operator-()const{return ModInt()-*this;}
	ModInt pow(int n)const{
		mint res(1),x(*this);
		while(n){
			if(n&1)res*=x;
			x*=x;
			n>>=1;
		}
		return res;
	}

    ModInt inv()const{return pow(mod-2);}
};


using mint=ModInt;

const int vcmax=(1<<21)+10;
mint fact[vcmax],finv[vcmax],invs[vcmax];
void initfact(){
	fact[0]=1;
	rng(i,1,vcmax){
		fact[i]=fact[i-1]*i;
	}
	finv[vcmax-1]=fact[vcmax-1].inv();
	for(int i=vcmax-2;i>=0;i--){
		finv[i]=finv[i+1]*(i+1);
	}
	for(int i=vcmax-1;i>=1;i--){
		invs[i]=finv[i]*fact[i-1];
	}
}
mint choose(int n,int k){
	return fact[n]*finv[n-k]*finv[k];
}
mint binom(int a,int b){
	return fact[a+b]*finv[a]*finv[b];
}
mint catalan(int n){
	return binom(n,n)-(n-1>=0?binom(n-1,n+1):0);
}

#define USE_FMT
//998244353
const mint prim_root=3;

/*
//in-place fft
//size of input must be a power of 2
void inplace_fmt(vector<mint>&f,const bool inv){
	const int n=f.size();
	const mint root=inv?prim_root.inv():prim_root;
	vc<mint> g(n);
	for(int b=n/2;b>=1;b/=2){
		mint w=root.pow((mint::base-1)/(n/b)),p=1;
		for(int i=0;i<n;i+=b*2){
			rep(j,b){
				f[i+j+b]*=p;
				g[i/2+j]=f[i+j]+f[i+b+j];
				g[n/2+i/2+j]=f[i+j]-f[i+b+j];
			}
			p*=w;
		}
		swap(f,g);
	}
	if(inv)rep(i,n)
		f[i]*=inv[n];
}*/

static const int LG=21;
mint roots[1<<(LG+1)],iroots[1<<(LG+1)];
struct PrepareRoots{
	PrepareRoots(){
		rep(w,LG+1){
			const int s=(1<<w)-1;
			const mint g=prim_root.pow((mod-1)/(1<<w)),ig=g.inv();
			mint p=1,ip=1;
			rep(i,1<<w){
				roots[s+i]=p;p*=g;
				iroots[s+i]=ip;ip*=ig;
			}
		}
	}
} PrepareRootsDummy;

void broken_fmt(vc<mint>&f){
	const int n=f.size();
	for(int b=n/2;b>=1;b/=2){
		for(int i=0;i<n;i+=b*2){
			rep(j,b){
				mint tmp=f[i+j]-f[i+j+b];
				f[i+j]+=f[i+j+b];
				f[i+j+b]=tmp*roots[b*2-1+j];
			}
		}
	}
}

void broken_ifmt(vc<mint>&f){
	const int n=f.size();
	for(int b=1;b<=n/2;b*=2){
		for(int i=0;i<n;i+=b*2){
			rep(j,b){
				f[i+j+b]*=iroots[b*2-1+j];
				mint tmp=f[i+j]-f[i+j+b];
				f[i+j]+=f[i+j+b];
				f[i+j+b]=tmp;
			}
		}
	}
	rep(i,n)
		f[i]*=invs[n];
}

void inplace_fmt(vector<mint>&f,const bool i){
	if(!i)broken_fmt(f);
	else broken_ifmt(f);
}

vc<mint> multiply(vc<mint> x,vc<mint> y,bool same=false){
	int n=x.size()+y.size()-1;
	int s=1;
	while(s<n)s*=2;
	x.resize(s);inplace_fmt(x,false);
	if(!same){
		y.resize(s);inplace_fmt(y,false);
	}else
		y=x;
	rep(i,s)
		x[i]*=y[i];
	inplace_fmt(x,true);x.resize(n);
	return x;
}

template<class D>
struct Poly:public vc<D>{
	template<class...Args>
	Poly(Args...args):vc<D>(args...){}
	Poly(initializer_list<D>init):vc<D>(all(init)){}
	int size()const{
		return vc<D>::size();
	}
	void ups(int s){
		if(size()<s)this->resize(s,0);
	}
	Poly low(int s)const{
		return Poly(this->bg,this->bg+min(max(s,int(1)),size()));
	}
	Poly rev()const{
		auto r=*this;
		reverse(all(r));
		return r;
	}
	Poly& operator+=(const Poly&r){
		ups(r.size());
		rep(i,r.size())
			(*this)[i]+=r[i];
		return *this;
	}
	Poly& operator-=(const Poly&r){
		ups(r.size());
		rep(i,r.size())
			(*this)[i]-=r[i];
		return *this;
	}
	template<class T>
	Poly& operator*=(T t){
		for(auto&v:*this)
			v*=t;
		return *this;
	}
	Poly& operator*=(const Poly&r){
		return *this=multiply(*this,r);
	}
	Poly square()const{
		return multiply(*this,*this,true);
	}
	#ifndef USE_FMT
	Poly inv(int s)const{
		Poly r{1/(*this)[0]};
		for(int n=1;n<s;n*=2)
			r=r*2-(r.square()*low(2*n)).low(2*n);
		return r.low(s);
	}
	#else
	Poly inv(int s)const{
		Poly r{D(1)/(*this)[0]};
		for(int n=1;n<s;n*=2){
			r.resize(n*4);
			inplace_fmt(r,false);
			vc<D> f=low(2*n);
			f.resize(n*4);
			inplace_fmt(f,false);
			rep(i,n*4)
				r[i]=r[i]*2-r[i]*r[i]*f[i];
			inplace_fmt(r,true);
			r.resize(2*n);
		}
		return r.low(s);
	}
	#endif
	template<class T>
	Poly& operator/=(T t){
		return *this*=D(1)/D(t);
	}
	Poly quotient(const Poly&r,const Poly&rri)const{
		int m=r.size();
		assert(r[m-1]);
		int n=size();
		int s=n-m+1;
		if(s<=0) return {0};
		return (rev().low(s)*rri.low(s)).low(s).rev();
	}
	Poly& operator/=(const Poly&r){
		return *this=quotient(r,r.rev().inv(max(size()-r.size(),int(0))+1));
	}
	Poly& operator%=(const Poly&r){
		*this-=*this/r*r;
		return *this=low(r.size()-1);
	}
	Poly operator+(const Poly&r)const{return Poly(*this)+=r;}
	Poly operator-(const Poly&r)const{return Poly(*this)-=r;}
	template<class T>
	Poly operator*(T t)const{return Poly(*this)*=t;}
	Poly operator*(const Poly&r)const{return Poly(*this)*=r;}
	template<class T>
	Poly operator/(T t)const{return Poly(*this)/=t;}
	Poly operator/(const Poly&r)const{return Poly(*this)/=r;}
	Poly operator%(const Poly&r)const{return Poly(*this)%=r;}
	Poly dif()const{
		Poly r(max(int(0),size()-1));
		rep(i,r.size())
			r[i]=(*this)[i+1]*(i+1);
		return r;
	}
	Poly inte()const{
		Poly r(size()+1,0);
		rep(i,size())
			r[i+1]=(*this)[i]*invs[i+1];
		return r;
	}
	//opencupXvcIII GP of Peterhof H
	Poly log(int s)const{
		return (low(s).dif()*inv(s-1)).low(s-1).inte();
	}
	//Petrozavodsk 2019w Day1 G
	Poly exp(int s)const{
		return exp2(s).a;
	}
	pair<Poly,Poly> exp2(int s)const{
		assert((*this)[0]==mint(0));
		Poly f{1},g{1};
		for(int n=1;;n*=2){
			if(n>=s)break;
			g=g*2-(g*g*f).low(n);
			//if(n>=s)break;
			Poly q=low(n).dif();
			q=q+g*(f.dif()-f*q).low(2*n-1);
			f=f+(f*(low(2*n)-q.inte())).low(2*n);
		}
		return mp(f.low(s),g.low(s));
	}
	//CF250 E
	Poly sqrt(int s)const{
		assert((*this)[0]==1);
		Poly r{1};
		for(int n=1;n<s;n*=2)
			r=(r+(r.inv(n*2)*low(n*2)).low(n*2))*inv[2];
		return r.low(s);
	}
	pair<Poly,Poly> divide(const Poly&r,const Poly&rri)const{
		Poly a=quotient(r,rri);
		Poly b=*this-a*r;
		return mp(a,b.low(r.size()-1));
	}
	//Yukicoder No.215
	Poly pow_mod(int n,const Poly&r)const{
		Poly rri=r.rev().inv(r.size());
		Poly cur{1},x=*this%r;
		while(n){
			if(n%2)
				cur=(cur*x).divide(r,rri).b;
			x=(x*x).divide(r,rri).b;
			n/=2;
		}
		return cur;
	}
	D eval(D x)const{
		D r=0,w=1;
		for(auto v:*this){
			r+=w*v;
			w*=x;
		}
		return r;
	}
};

signed main(){
	cin.tie(0);
	ios::sync_with_stdio(0);
	cout<<fixed<<setprecision(20);
	
	initfact();
	
	int n,m;cin>>n>>m;
	Poly<mint> f(n+1);
	rep(i,n+1)f[i]=mint(n+1-i)*finv[i];
	
	mint w=f[0];
	dmp(f);
	f/=w;
	auto g=f.log(n+1)*m;
	auto h=g.exp(n+1)*w.pow(m);
	dmp(h);
	
	mint ans=0;
	rep(i,n+1)ans+=h[i]*finv[n-i];
	
	cout<<(ans*fact[n]).a<<endl;
}


Compiler output:
a.cc: In member function 'ModInt ModInt::pow(ll) const':
a.cc:203:17: error: 'mint' was not declared in this scope; did you mean 'uint'?
  203 |                 mint res(1),x(*this);
      |                 ^~~~
      |                 uint
a.cc:205:32: error: 'res' was not declared in this scope; did you mean 'yes'?
  205 |                         if(n&1)res*=x;
      |                                ^~~
      |                                yes
a.cc:205:37: error: 'x' was not declared in this scope
  205 |                         if(n&1)res*=x;
      |                                     ^
a.cc:206:25: error: 'x' was not declared in this scope
  206 |                         x*=x;
      |                         ^
a.cc:209:24: error: 'res' was not declared in this scope; did you mean 'yes'?
  209 |                 return res;
      |                        ^~~
      |                        yes