#include<bits/stdc++.h>
#define rp(i,a,b) for(int i=a;i<=b;++i)
#define pr(i,a,b) for(int i=a;i>=b;--i)
using namespace std;
//xiaoyaowudi
constexpr int N(2010),p(998244353);
int n,x[N];
void init(){
	std::ios::sync_with_stdio(false);
	std::cin.tie(nullptr);
	int m,cnt(0);
	std::cin>>n>>m;
	static bool hv[N];
	static std::bitset<N> b[N];
	static std::bitset<N> a[N],xb;
	for(int i(1);i<=n;++i)
	{
		static char s[N];std::cin>>s;
		for(int j(0);j<m;++j)
		{
			a[i][m-j-1]=(s[j]=='1');
		}
		bool st(false);
		for(int j(m-1);j>=0;--j) if(a[i][j])
		{
			if(hv[j])
			{
				a[i]^=b[j];
			}
			else
			{
				hv[j]=st=true;
				b[j]=a[i];
				break;
			}
		}
		if(!st){std::cout<<0<<std::endl;exit(0);}
	}
	{
		static char s[N];std::cin>>s;
		for(int j(0);j<m;++j) xb[m-j-1]=(s[j]=='1');
	}
	for(int i(m-1);i>=0;--i) if(hv[i]) for(int j(i+1);j<m;++j) if(hv[j] && b[j][i]) b[j]^=b[i];
	static std::bitset<N> cur;
	for(int j(m-1);j>=0;--j) if(hv[j])
	{
		std::bitset<N> nw(cur^b[j]);
		bool cap(true);
		for(int t(m-1);t>=0;--t) if(xb[t]!=nw[t])
		{
			if(xb[t]<nw[t]) cap=false;
			break;
		}
		if(cap) cur=nw,x[++cnt]=1;
		else x[++cnt]=0;
	}
	if(!x[1]){std::cout<<0<<std::endl;exit(0);}
}
//~xiaoyaowudi
typedef long long ll;
constexpr int q(p-1);
inline int inc(int x,int y){
	return x+=y-p,x+=x>>31&p;
}
inline int dec(int x,int y){
	return x-=y,x+=x>>31&p;
}
inline int mul(int x,int y){
	return ll(x)*y%p;
}
inline void upd(int&x,int y){
	x=inc(x,y);
}
int ksm(int x,int y){
	int z=1;
	for(;y;y>>=1,x=mul(x,x))if(y&1)z=mul(x,z);
	return z;
}
int ksm_e(int x,int y){
	int z=1;
	for(;y;y>>=1,x=ll(x)*x%q)if(y&1)z=ll(x)*z%q;
	return z;
}
int v[N],w[N],iw[N],wx[N][2],a2[N],i2[N],h[N][N],g[N][N][2],f[N][N][4],a[N],b[N],c[N];
void init_val(){
	rp(i,0,n){
		v[i]=ksm(2,ksm_e(2,i));
		w[i]=ksm(2,i);
		iw[i]=ksm(w[i],p-2);
		wx[i][0]=w[i];
		wx[i][1]=0;
	}
	a2[0]=1;
	rp(i,1,n){
		a2[i]=mul(a2[i-1],w[i]-1);
	}
	i2[n]=ksm(a2[n],p-2);
	pr(i,n,1){
		i2[i-1]=mul(i2[i],w[i]-1);
	}
}
int main(){
	// freopen("1.in","r",stdin);
	init();
	init_val();
	/*
	rp(i,1,n){
		printf("%d",x[i]);
	}
	puts("");
	*/
	h[n+1][0]=1;
	pr(i,n,2){
		rp(j,0,n-i){
			int u=mul(v[j],w[n-i-j]);
			h[i][j]=inc(h[i][j],h[i+1][j]);
			h[i][j+1]=inc(h[i][j+1],mul(u,h[i+1][j]));
		}
	}
	g[n+1][0][0]=1;
	g[n+1][0][1]=1;
	pr(i,n,2){
		rp(j,0,n-i){
			rp(k,0,1){
				int t=mul(w[n-i-j],k&&!x[i]?1:v[j]);
				upd(g[i][j][k],g[i+1][j][k]);
				upd(g[i][j+1][k],mul(t,g[i+1][j][k]));
			}
		}
		if(x[i]){
			rp(j,0,n-i){
				upd(g[i][j][1],mul(w[n-i-j],g[i+1][j][0]));
			}
		}
	}
	f[n+1][0][0]=1;
	f[n+1][0][1]=1;
	pr(i,n,2){
		rp(j,0,n-i){
			rp(k,0,3){
				int u=mul(w[n-i-j],k==3&&!x[i]?1:v[j]);
				upd(f[i][j][k],f[i+1][j][k]);
				if(!k||k==3||!x[i]){
					upd(f[i][j+1][k],mul(u,f[i+1][j][k]));
				}
			}
			if(x[i]){
				upd(f[i][j+1][1],mul(mul(w[n-i-j],v[j]),f[i+1][j][0]));
				upd(f[i][j+1][3],mul(w[n-i-j],f[i][j][2]));
			}else{
				upd(f[i][j][2],mul(w[n-i-j],f[i+1][j][1]));
			}
		}
	}
	a[0]=a2[n];
	rp(j,1,n){
		int x=inc(h[2][j],mul(v[j-1],g[2][j-1][1]));
		int y=inc(f[2][j-1][2],mul(v[j-1],f[2][j-1][3]));
		a[j]=mul(inc(x,y),a2[n-j]);
	}
	rp(i,0,n){
		int u=mul(i2[i],ksm(2,i*(i-1)/2));
		b[i]=i&1?p-u:u;
	}
	rp(i,0,n){
		rp(j,0,i){
			c[i]=inc(c[i],mul(b[j],a[i-j]));
		}
	}
	printf("%d\n",c[n]);
	return 0;
}