#include<bits/stdc++.h>
using namespace std;
#define ll long long
const int MOD=998244353;
struct modint{
int x;
modint(int y=0){x=y;}
};
modint operator +(modint x,modint y){return modint(x.x+y.x>=MOD?x.x+y.x-MOD:x.x+y.x);}
modint operator -(modint x,modint y){return (x.x<y.x?x.x-y.x+MOD:x.x-y.x);}
modint operator ^(modint x,int y){ll a=x.x,r=1;while(y){if(y&1)r=r*a%MOD;a=a*a%MOD,y>>=1;}return modint(r);}
modint operator *(modint x,modint y){return modint(1ll*x.x*y.x%MOD);}
modint operator /(modint x,modint y){return x*(y^(MOD-2));}
modint operator /(modint x,int y){return x/modint(y);}
modint operator *(modint x,int y){return modint(1ll*x.x*y%MOD);}
void operator +=(modint &x,modint y){x=(x+y);}
const int MAXN=2005;
int n,m;
bitset<MAXN> bas[MAXN],fin;
modint f[MAXN][MAXN],g[MAXN][MAXN],h[MAXN];
modint pw2[MAXN],pwpw2[MAXN],fac2[MAXN],inf2[MAXN];
modint C2(int x,int y){return x<0||x>y?modint(0):inf2[x]*inf2[y-x]*fac2[y];}
modint sgn(int x){return (x&1)?modint(MOD-1):modint(1);}
int main(){
	ios::sync_with_stdio(false);
	// freopen("Otomachi_Una.in","r",stdin);
	// freopen("Otomachi_Una.out","w",stdout);
	cin>>n>>m;
	for(int i=1;i<=n;i++){
		string s;cin>>s;
		bitset<MAXN> my;
		for(int i=1;i<=m;i++) my[i]=(s[m-i]=='1');
		bool flag=false;
		for(int j=m;j>=1;j--) if(my[j]){
			if(bas[j].any()) my^=bas[j];
			else{
				bas[j]=my;
				flag=true;
				break;
			}
		}
		if(!flag){
			cout<<0;
			return 0;
		}
	}
	for(int i=1;i<=m;i++) if(bas[i].any()){
		for(int j=1;j<i;j++) if(bas[i][j]&&bas[j].any()) bas[i]^=bas[j];
	}
	bitset<MAXN> my,et;
	string s;cin>>s;
	for(int i=1;i<=m;i++) my[i]=(s[m-i]=='1');
	int n0=0;
	for(int i=m;i>=1;i--) if(bas[i].any()){
		et^=bas[i];
		bool flag=true;
		for(int j=m;j>=1;j--) if(my[j]!=et[j]){
			flag=(my[j]>et[j]);
			break;
		}
		fin[n0++]=flag;
		if(!flag) et^=bas[i];
	}
	if(!fin[0]){
		cout<<0;
		return 0;
	}
	pw2[0]=fac2[0]=inf2[0]=modint(1);pwpw2[0]=modint(2);
	for(int i=1;i<MAXN;i++){
		pw2[i]=pw2[i-1]*2;
		fac2[i]=fac2[i-1]*(pw2[i]-modint(1));
		inf2[i]=inf2[i-1]/(pw2[i]-modint(1));
		pwpw2[i]=pwpw2[i-1]*pwpw2[i-1];
	}
	// f[i][j] 前 i 位当中已经选了 j 位，且未顶到，钦定 pos[n] 以选
	// g[i][j] 前 i 为当中已经选了 j 位，且顶到
	f[0][0]=modint(1);g[0][0]=modint(2);
	for(int i=0;i<n;i++) for(int j=0;j<=i;j++) if(f[i][j].x||g[i][j].x){
		// from f[i][j] or g[i][j]
		if(fin[n-1-i]){
			// 这个位置上有值 desu~
			if(i==n-1){
				g[i+1][j+1]+=g[i][j]*pw2[i-j]*pwpw2[j];
				continue;
			}
			// 不选，这位当前是 0
			g[i+1][j]+=f[i][j]*pwpw2[j]/2;
			f[i+1][j]+=f[i][j]/2;
			// 不选，这位当前是 1
			f[i+1][j]+=f[i][j]/2;
			g[i+1][j]+=g[i][j]/2;
			// 选！
			f[i+1][j+1]+=f[i][j]*pw2[i-j];
			g[i+1][j+1]+=g[i][j]*pw2[i-j]*pwpw2[j];
		}else{
			// 选！
			f[i+1][j+1]+=f[i][j]*pw2[i-j];
			g[i+1][j+1]+=g[i][j]*pw2[i-j];
			// 不选，这位当前是 1
			f[i+1][j]+=f[i][j]/2;
			g[i+1][j]+=f[i][j]/2;
			// 不选，当前这位是 0
			f[i+1][j]+=f[i][j]/2;
			g[i+1][j]+=g[i][j]/2;
		}
	}
	h[0]=2;
	for(int i=1;i<=n;i++) h[i]=g[n][i]+pwpw2[i]*C2(i,n-1);
	modint ans;
	// q- 二项式反演 desu~
	for(int i=0;i<=n;i++) ans+=h[i]*sgn(n-i)*(modint(2)^((n-i)*(n-i-1)/2));
	ans=ans/2;
	cout<<ans.x<<'\n';
}