#define G 3
#include<map>
#include<set>
#include<ctime>
#include<cmath>
#include<queue>
#include<bitset>
#include<cstdio>
#include<vector>
#include<random>
#include<cstdlib>
#include<cstring>
#include<iostream>
#include<algorithm>
#define ll long long
using namespace std;
#define I ll
#define her1 20081214
#define IV void
#define cht 998244353
#define ld long double
#define Aestas16 392699
#define ull unsigned long long
#define cp(x,y)memcpy(x,y,sizeof y)
#define mem(x,val)memset(x,val,sizeof x)
#define D(i,j,n)for(register int i=j;i>=n;i--)
#define E(i,now)for(register int i=first[now];i;i=e[i].nxt)
#define F(i,j,n)for(register int i=j;i<=n;i++)
#define DL(i,j,n)for(register i64 i=j;i>=n;i--)
#define EL(i,now)for(register i64 i=first[now];i;i=e[i].nxt)
#define FL(i,j,n)for(register i64 i=j;i<=n;i++)
//#define D(i,j,n)for(int i=j;i>=n;i--)
//#define E(i,now)for(int i=first[now];i;i=e[i].nxt)
//#define F(i,j,n)for(int i=j;i<=n;i++)
//#define DL(i,j,n)for(register ll i=j;i>=n;i--)
//#define EL(i,now)for(register ll i=first[now];i;i=e[i].nxt)
//#define FL(i,j,n)for(register ll i=j;i<=n;i++)
ll read(){
	ll ans=0,f=1;
	char c=getchar();
	while(c<'0'||c>'9'){
		if(c=='-')f=-1;
		c=getchar();
	}
	while(c>='0'&&c<='9')ans=ans*10+c-'0',c=getchar();
	return ans*f;
}
#undef ll
#include "assert.h"
mt19937_64 rnd(her1);
#include "functional"
using i64 = long long;
const int MAX = 2e5;
const int maxn = 2e5+5;
const int maxm = 6e5+5;
#define in(i,V) F(i,0,(i64)V.size()-1)
#define My_assert(expr,tips) ((expr)?(void(0)):(puts(tips),exit(0)))
IV cadd(i64&x,i64 val){x=(x+val)%cht;}

i64 w[maxm];
i64 qpow(i64 n,i64 base=cht-2){
	i64 ans=1;
	while(base){
		if(base&1)ans=ans*n%cht;
		n=n*n%cht;base>>=1;
	}
	return ans;
}
IV init(i64 limit){
	for(int i=1,j,k;i<limit;i<<=1)
		for(w[j=i]=1,k=qpow(3,(cht-1)/(i<<1)),j++;j<(i<<1);j++)
			w[j]=w[j-1]*k%cht;
}
const i64 invG = qpow(G);
IV DIT(i64*a,i64 limit){
	for(i64 i,j,k=limit>>1,L,*W,*x,*y,z;k;k>>=1)
		for(L=k<<1,i=0;i<limit;i+=L)for(j=0,W=w+k,x=a+i,y=x+k;j<k;j++,W++,x++,y++)
			*y=(*x+cht-(z=*y))* *W%cht,*x=(*x+z)%cht;
}
IV DIF(i64*a,i64 limit){
	for(i64 i,j,k=1,L,*W,*x,*y,z;k<limit;k<<=1)
		for(L=k<<1,i=0;i<limit;i+=L)for(j=0,W=w+k,x=a+i,y=x+k;j<k;j++,W++,x++,y++)
			z=1ll* *W* *y%cht,*y=(*x-z)%cht,*x=(*x+z)%cht;
	reverse(a+1,a+limit);
	i64 inv=qpow(limit);
	F(i,0,limit-1)a[i]=a[i]*inv%cht;
}
IV NTT(i64*a,i64 limit,i64 type){
	static i64 rev[maxm];
	i64 sb=__lg(limit);
	F(i,0,limit-1)rev[i]=(rev[i>>1]>>1)|((i&1)<<sb-1);
	F(i,0,limit-1)if(i<rev[i])swap(a[i],a[rev[i]]);
	for(int p=2;p<=limit;p<<=1){
		i64 wG=qpow(type?invG:G,(cht-1)/p),k=(p>>1);
		for(i64 l=0,w=1;l<limit;l+=p,w=1)F(i,l,l+k-1){
			i64 x=a[i],y=a[i+k]*w%cht;
			a[i]=(x+y)%cht;a[i+k]=(x-y+cht)%cht;w=w*wG%cht;
		}
	}
	if(type){
		i64 inv=qpow(limit);
		F(i,0,limit-1)a[i]=a[i]*inv%cht;
	}
}
#define poly vector<i64>

poly operator*(const poly&A,const poly&B){
	static i64 f[maxm],g[maxm];
	My_assert(A.size()&&B.size(),"multiply with a empty poly.");
	i64 limit=1;
	while(limit<=A.size()+B.size())
		limit<<=1;
	F(i,0,limit-1)f[i]=g[i]=0;
	in(i,A)f[i]=A[i];in(i,B)g[i]=B[i];
	DIT(f,limit);DIT(g,limit);
	F(i,0,limit-1)f[i]=f[i]*g[i]%cht;DIF(f,limit);
	poly C;C.resize(A.size()+B.size()-1);
	in(i,C)C[i]=f[i];
	return C;
}
poly operator+(const poly&A,const poly&B){
	poly C;C.resize(max(A.size(),B.size()));
	in(i,C)C[i]=0;
	in(i,A)cadd(C[i],A[i]);
	in(i,B)cadd(C[i],B[i]);
	return C;
}
poly operator-(const poly&A,const poly&B){
	poly C;C.resize(max(A.size(),B.size()));
	in(i,C)C[i]=0;
	in(i,A)cadd(C[i],A[i]);
	in(i,B)cadd(C[i],-B[i]);
	return C;
}

i64 fac[maxn],ifac[maxn];
i64 C(i64 n,i64 m){
	if(n<m||n<0||m<0)return 0;
	return fac[n]*ifac[m]%cht*ifac[n-m]%cht;
}
IV init(){
	fac[0]=1;F(i,1,MAX)fac[i]=fac[i-1]*i%cht;
	ifac[MAX]=qpow(fac[MAX]);D(i,MAX-1,0)ifac[i]=ifac[i+1]*(i+1)%cht;
}
IV remod(poly&A,i64 n){while(A.size()>n)A.pop_back();}

i64 n,k,wi[1<<3],S,f[maxn][4];
i64 upd(i64 z,i64 x){return(z|x<<k-2)>>1;}
i64 c[4][4][1<<18],c2[4][4][1<<19];
i64 sv[4][1<<18];
IV cdq(i64 l,i64 r){
	if(l==r)return;i64 mid=l+r>>1;
	cdq(l,mid);

	i64 L=1;while(L<=(r-l)*2)L<<=1;
	F(x,0,S)F(i,0,L-1)sv[x][i]=0;
	// puts("??");
	F(x,0,S){
		static i64 a[1<<18];
		F(i,0,L-1)a[i]=0;F(i,l,mid)a[i-l]=f[i][x];
		DIT(a,L);
		// if(l==2&&r==6){
		// 	F(i,0,L-1)cout<<a[i]<<' ';puts("");
		// 	F(i,0,L-1)cout<<c2[x][0][L+i]<<' ';puts("");
		// }
		F(y,0,S)F(i,0,L-1)cadd(sv[y][i],c2[x][y][L+i]*a[i]);
	}
	// cout<<l<<' '<<mid<<' '<<r<<endl;
	// F(x,0,S){
	// 	F(i,0,L-1)cout<<sv[x][i]<<' ';puts("");
	// }
	F(x,0,S)DIF(sv[x],L);
	// F(x,0,S){
	// 	F(i,0,L-1)cout<<sv[x][i]<<' ';puts("");
	// }
	F(i,mid+1,r)F(x,0,S)
		cadd(f[i][x],sv[x][i-l]);

	cdq(mid+1,r);
}
int main(){
	// freopen("1.in","r",stdin);
	// freopen("1.out","w",stdout);

	init();init(1<<18);
	n=read();k=read();S=(1<<k-2)-1;
	F(s,0,S*2+1)wi[s]=read();f[0][0]=1;
	F(i,0,k-1){
		F(s,0,S)if(f[i][s]){
			i64 tmp[4];mem(tmp,0);
			tmp[upd(s,0)]=f[i][s]*(i+1>=k?wi[s]:1)%cht;
				// F(z,0,S)cout<<tmp[z]<<' ';puts("");
			F(j,i+1,n){
				F(z,0,S)cadd(f[j][z],tmp[z]*ifac[j-i]);
				i64 ntmp[4];mem(ntmp,0);
				F(z,0,S){
					cadd(ntmp[upd(z,0)],-tmp[z]*(j+1>=k?wi[z]:1));
					cadd(ntmp[upd(z,1)],tmp[z]*(j+1>=k?wi[z|(1<<k-2)]:1));
					// cout<<(z|(1<<k-2))<<' '<<wi[z|(1<<k-2)]<<endl;
				}
				F(z,0,S)tmp[z]=ntmp[z];
			}
		}
	}
	// F(i,0,n)
	// F(s,0,S)if(f[i][s]){
	// 	cout<<i<<' '<<s<<' '<<f[i][s]<<endl;
	// }
	F(s,0,S){
		i64 tmp[4];mem(tmp,0);tmp[upd(s,0)]=wi[s];
		F(i,1,n){
			F(z,0,S)cadd(c[s][z][i],tmp[z]*ifac[i]);
			i64 ntmp[4];mem(ntmp,0);
			F(z,0,S){
				cadd(ntmp[upd(z,0)],-tmp[z]*wi[z]);
				cadd(ntmp[upd(z,1)],tmp[z]*wi[z|(1<<k-2)]);
			}
			F(z,0,S)tmp[z]=ntmp[z];
		}
	}
	// F(i,1,n)cout<<c[0][0][i]<<' ';puts("");
	F(x,0,S)F(y,0,S)for(int L=2;L<=4*(n+1);L<<=1){
		static i64 T[maxn];
		F(i,0,L-1)T[i]=c[x][y][i];DIT(T,L);
		F(i,0,L-1)c2[x][y][L+i]=T[i];
		// cout<<"?"<<L<<endl;
		// F(i,0,L-1)cout<<T[i]<<' ';puts("");
	}
	// F(i,0,100)cout<<c2[0][0][i]<<' ';puts("");
	cdq(k,n);
	// F(i,0,n)
	// F(s,0,S)if(f[i][s]){
	// 	cout<<i<<' '<<s<<' '<<f[i][s]<<endl;
	// }
	i64 Ans=0;F(z,0,S)cadd(Ans,f[n][z]);
	cout<<(Ans*fac[n]%cht+cht)%cht;
	return 0;
}