#include<bits/stdc++.h>
#define LL long long
#define LLL __int128
#define uint unsigned
#define ldb long double
#define uLL unsigned long long
using namespace std;
typedef vector<int> poly;
typedef vector<int> Vec;
typedef vector<Vec> Mat;
typedef tuple<poly,poly,poly,poly> Mat2;
mt19937 rng(chrono::system_clock::now().time_since_epoch().count());
const int Mod=998244353,G=3;
vector<uLL>Grt,iGrt;
poly Tr,frc({1,1}),inv({0,1}),ivf({1,1});
inline int qpow(int x,int y,int z=1){
	for(;y;(y>>=1)&&(x=(LL)x*x%Mod))if(y&1)z=(LL)z*x%Mod;return z;
}
inline void Init(const int&n){
	for(int i=frc.size();i<=n;++i)
		frc.emplace_back((LL)frc.back()*i%Mod),
		inv.emplace_back(Mod-Mod/i*(LL)inv[Mod%i]%Mod),
		ivf.emplace_back((LL)ivf.back()*inv.back()%Mod);
}
inline int Binom(const int&n,const int&m){
	if(n<m||m<0)return 0;
	return Init(n),(LL)frc[n]*ivf[m]%Mod*ivf[n-m]%Mod;
}
inline bool Empty(poly&P){
	for(;!P.empty()&&!P.back();P.pop_back());
	return P.empty();
}
inline poly Add(poly P,poly Q){
    if(P.size()<Q.size())P.swap(Q);
    for(int i=Q.size();i--;)(P[i]+=Q[i])>=Mod&&(P[i]-=Mod);
    return P;
}
inline poly Add_Empty(poly P,poly Q){
    if(P.size()<Q.size())P.swap(Q);
    for(int i=Q.size();i--;)(P[i]+=Q[i])>=Mod&&(P[i]-=Mod);
    return Empty(P),P;
}
inline poly Sub(poly P,poly Q){
    if(P.size()<Q.size())P.resize(Q.size());
    for(int i=Q.size();i--;)(P[i]-=Q[i])<0&&(P[i]+=Mod);
    return P;
}
inline poly Sub_Empty(poly P,poly Q){
    if(P.size()<Q.size())P.resize(Q.size());
    for(int i=Q.size();i--;)(P[i]-=Q[i])<0&&(P[i]+=Mod);
    return Empty(P),P;
}
inline poly Mulx(poly P,int x){
	for(int&i:P)i=(LL)i*x%Mod;
	return P;
}
inline poly Neg(poly P){
	for(int i=P.size();i--;)P[i]&&(P[i]=Mod-P[i]);
	return P;
}
inline int Eval(poly&P,int x){
	int z=0;
	for(int i=P.size();i--;)z=((LL)z*x+P[i])%Mod;
	return z;
}
inline poly invLinear(poly P){
	const int n=P.size();
	poly Q(n+1,1);
	for(int i=0;i<n;++i)Q[i+1]=(LL)Q[i]*P[i]%Mod;
	int t=qpow(Q[n],Mod-2);Q.pop_back();
	for(int i=n;i--;)Q[i]=(LL)Q[i]*t%Mod,t=(LL)t*P[i]%Mod;
	return Q;
}
inline Mat operator*(const Mat&x,const Mat&y){
	const int n=x.size(),m=y.size(),q=y[0].size();
	Mat z(n,Vec(q));
	for(int i=0;i<n;++i)for(int j=0;j<m;++j)if(x[i][j])
		for(int k=0;k<q;++k)z[i][k]=(z[i][k]+(LL)x[i][j]*y[j][k])%Mod;
	return z;
}
inline uLL trans(const uLL&x){
    constexpr uLL A=-(uLL)Mod/Mod+1;
    constexpr uLL Q=(((__uint128_t)(-(uLL)Mod%Mod)<<64)+Mod-1)/Mod;
    return x*A+(uLL)((__uint128_t)x*Q>>64)+1;
}
inline uLL qmul(const uLL&x,const uLL&y){
    return x*y*(__uint128_t)Mod>>64;
}
inline int mul(const int&x,const int&y){
	return qmul(x,trans(y));
}
inline int add(int x,const int&y){
    return ((x+=y)-Mod)>=0?x-Mod:x;
}
inline int sub(int x,const int&y){
    return (x-=y)<0?x+Mod:x;
}
inline int div2(const int&x){
    return x&1?(x+Mod)>>1:x>>1;
}
inline void extend(const int&n){
    if(Grt.empty())Grt.emplace_back(trans(1)),iGrt.emplace_back(trans(1));
    if(Grt.size()<n){
        int L=Grt.size();
        Grt.resize(n),iGrt.resize(n);
        for(;L<n;L*=2){
            const int w=qpow(G,Mod/(L*4)),iw=qpow(w,Mod-2);
            for(int i=0;i<L;++i)Grt[i+L]=trans(qmul(Grt[i],w)),iGrt[i+L]=trans(qmul(iGrt[i],iw));
        }
    }
}
template<int A,int B,int C=0,class fun>inline void Butterrep(int i,int j,int k,fun F){
    if(A!=C)F(i,j+C/B,k+C*2-C%B),Butterrep<A,B,C+(C<A)>(i,j,k,F);
}
template<class fun>inline void ButterX(int i,int n,fun F){
    for(int j=0;2*i*j<n;++j)for(int k=0;k<i;k+=32)Butterrep<32,32>(i,j,k+2*i*j,F);
}
template<int i,class fun>inline void ButterY(int n,fun F){
    if(n>32)for(int j=0;2*i*j<n;j+=32/i)Butterrep<32,i>(i,j,2*i*j,F);
    else if(i<n)for(int j=0;2*i*j<n;++j)for(int k=0;k<i;++k)F(i,j,k+2*i*j);
}
template<class T>inline void DFT(T P,int n){
    extend(n);
    const auto F=[&](int x,int y,int z){
        const int a=P[z],b=qmul(P[z+x],Grt[y]);
        P[z]=add(a,b),P[z+x]=sub(a,b);
    };
    for(int i=n>>1;i>16;i>>=1)ButterX(i,n,F);
    ButterY<16>(n,F),ButterY<8>(n,F),ButterY<4>(n,F),ButterY<2>(n,F),ButterY<1>(n,F);
}
template<class T>inline void IDFT(T P,int n){
    const uLL ni=trans(qpow(n,Mod-2));
	for(int i=0;i<n;++i)P[i]=qmul(P[i],ni);
    extend(n);
    const auto F=[&](int x,int y,int z){
        const int a=P[z],b=P[z+x];
        P[z]=add(a,b),P[z+x]=qmul(a-b+Mod,iGrt[y]);
    };
    ButterY<1>(n,F),ButterY<2>(n,F),ButterY<4>(n,F),ButterY<8>(n,F),ButterY<16>(n,F);
    for(int i=32;i<n;i<<=1)ButterX(i,n,F);
}
inline void DFT(poly&P){
	DFT(P.begin(),P.size());
}
inline void IDFT(poly&P){
	IDFT(P.begin(),P.size());
}
inline poly Mul(poly P,poly Q){
    if(P.empty()||Q.empty())return poly();
	const int pn=P.size(),qn=Q.size(),rn=pn+qn-1;
	const int m=2<<__lg(max(1,rn-1));
	P.resize(m),Q.resize(m);
	DFT(P),DFT(Q);
	for(int i=m;i--;)P[i]=(LL)P[i]*Q[i]%Mod;
	IDFT(P);
	return P.resize(rn),P;
}
inline poly MulT(poly P,poly Q){
	const int m=Q.size();
	reverse(Q.begin(),Q.end()),Q=Mul(P,Q);
	return poly(Q.begin()+m-1,Q.end());
}
inline poly Inv(poly P){
	const int pn=P.size();
	const int m=2<<__lg(max(1,pn-1));
	P.resize(m);
	poly Q({qpow(P[0],Mod-2)}),F,dQ;
	Q.reserve(m);
	for(int n=2;n<=m;n*=2){
		F=poly(P.begin(),P.begin()+n),dQ=Q;
		dQ.resize(n),DFT(dQ),DFT(F);
		for(int i=0;i<n;++i)F[i]=(LL)(Mod-F[i])*dQ[i]%Mod;
		IDFT(F),fill_n(F.begin(),n/2,0),DFT(F);
		for(int i=0;i<n;++i)dQ[i]=(LL)F[i]*dQ[i]%Mod;
		IDFT(dQ),Q.insert(Q.end(),dQ.begin()+n/2,dQ.end());
	}
	return Q.resize(pn),Q;
}
const int N=1e5+5,K=4,M=1<<(K-1);
int n,k,m,L,ans;
int a[K],W[M];
poly f[M][M],h[M];
inline int Less(int S){
	const int t=__lg(S);
	S^=1<<t;
	if(t==k-2)return S/2+((3<<k)>>3);
	else return S+(3<<t);
}
inline int LessW(int S){
	const int t=__lg(S);
	S^=1<<t;
	if(t==k-2)return W[(1<<(k-2))+S];
	else return 1;
}
inline int Greater(int S){
	const int t=__lg(S);
	S^=1<<t;
	if(t==k-2)return S/2+((2<<k)>>3);
	else return S+(2<<t);
}
inline int GreaterW(int S){
	const int t=__lg(S);
	S^=1<<t;
	if(t==k-2)return W[S];
	else return 1;
}
signed main(){
    cin.tie(0)->sync_with_stdio(0);
	cin>>n>>k,m=1<<(k-1),++n;
	Init(n);
	for(int i=0;i<m;++i)cin>>W[i];
	// cerr<<clock()<<endl;
	for(int S=1;S<m;++S)for(int T=1;T<m;++T)f[S][T].resize(n);
	for(int S=1;S<m;++S)f[S][Less(S)][1]=LessW(S);
	for(int i=2;i<n;++i)
		for(int S=1;S<m;++S)
			for(int T=1;T<m;++T){
				f[S][Less(T)][i]=sub(f[S][Less(T)][i],mul(f[S][T][i-1],LessW(T)));
				f[S][Greater(T)][i]=add(f[S][Greater(T)][i],mul(f[S][T][i-1],GreaterW(T)));
			}
	for(int S=1;S<m;++S)for(int T=1;T<m;++T)for(int i=1;i<n;++i)f[S][T][i]=mul(f[S][T][i],ivf[i]);
	for(int S=m/2;S<m;++S)for(int T=m/2;T<m;++T)f[S][T]=Neg(f[S][T]),Empty(f[S][T]);
	for(int S=m/2;S<m;++S)f[S][S].resize(n),f[S][S][0]=1;
	// cerr<<clock()<<endl;
	for(int i=m/2;i<m;++i){
		f[i][i]=Inv(f[i][i]);
		for(int j=m/2;j<m;++j)if(i!=j)
			if((f[i][j]=Mul(f[i][j],f[i][i])).size()>n)f[i][j].resize(n);
		for(int j=m/2;j<m;++j)if(i!=j)
			for(int k=m/2;k<m;++k)if(i!=k)
				if((f[j][k]=Sub(f[j][k],Mul(f[j][i],f[i][k]))).size()>n)f[j][k].resize(n);
		for(int j=m/2;j<m;++j)if(i!=j)
			if((f[j][i]=Neg(Mul(f[j][i],f[i][i]))).size()>n)f[j][i].resize(n);
	}
	// cerr<<clock()<<endl;
	for(int S=1;S<m;++S)h[S].resize(n);
	h[1][1]=1;
	for(int i=1;i<n;++i){
		for(int T=1;T<m;++T){
			h[Less(T)][i]=sub(h[Less(T)][i],mul(h[T][i-1],LessW(T)));
			h[Greater(T)][i]=add(h[Greater(T)][i],mul(h[T][i-1],GreaterW(T)));
		}
	}
	for(int T=1;T<m;++T)for(int i=1;i<n;++i)h[T][i]=mul(h[T][i],ivf[i]);
	for(int S=1;S<m/2;++S)for(int T=1;T<m;++T)
		Empty(h[S]),Empty(f[S][T]),h[T]=Add(h[T],Mul(h[S],f[S][T]));
	for(int S=m/2;S<m;++S)for(int T=m/2;T<m;++T){
		f[S][T].resize(n);
		for(int i=1;i<n;++i)ans=add(ans,mul(h[S][i],f[S][T][n-1-i]));
	}
	ans=mul(ans,frc[n-1]);
	// cerr<<clock()<<endl;
	cout<<ans<<'\n';
    return 0;
}
/*
40000 4
1 2 3 4 5 6 7 8
*/