#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef array<ull,32> arin;
#define fi first
#define se second
const ll mod=998244353;
ll pw(ll x,ll y){
	if(y==0) return 1;
	if(y%2) return x*pw(x,y-1)%mod;
	ll res=pw(x,y/2);
	return res*res%mod;
}
int n,m;
arin b[2001];
arin x;
bool nx[2001];
arin zero;
bool operator<(arin &x,arin &y){
	for(int k=(m-1)/64; k>=0 ;k--){
		if(x[k]!=y[k]) return x[k]<y[k];
	}
	return false;
}
arin operator+(arin x,arin y){
	arin z;
	for(int k=(m-1)/64; k>=0 ;k--) z[k]=x[k]^y[k];
	return z;
}
int get(arin &x,int j){
	return ((x[j>>6]>>(j&63))&1);
}
void out(arin &x){
	for(int i=m-1; i>=0 ;i--) cout << get(x,i);
	cout << '\n';
}

ll dps[2001][2001];
ll dpb[2001][2001];
ll p2[2001];
ll pp2[2001];
ll y[2001],z[2001];
int main(){
	ios::sync_with_stdio(false);cin.tie(0);
	cin >> n >> m;
	for(int i=1; i<=n ;i++){
		for(int j=m-1; j>=0 ;j--){
			char c;cin >> c;
			if(c=='1') b[i][j>>6]|=1ull<<(j&63);
		}
	}
	{
		for(int j=m-1; j>=0 ;j--){
			char c;cin >> c;
			if(c=='1') x[j>>6]|=1ull<<(j&63);
		}
	}
	int d=0;
	for(int j=m-1; j>=0 ;j--){
		if(d==n) continue; 
		for(int i=d+1; i<=n ;i++){
			if(get(b[i],j)){
				swap(b[i],b[d+1]);
				break;
			}
		}
		if(!get(b[d+1],j)) continue;
		d++;
		for(int i=1; i<=n ;i++){
			if(i==d) continue;
			if(get(b[i],j)) b[i]=b[i]+b[d];
		}
	}
	if(d!=n) return cout << "0\n",0;//not lin ind
	//m is no longer useful from now on
	arin cur=zero;
	p2[0]=1;
	pp2[1]=2;
	for(int i=1; i<=n ;i++){
		p2[i]=p2[i-1]*2%mod;
		if(i!=1) pp2[i]=pp2[i-1]*pp2[i-1]%mod;
		y[i]=pw(pp2[i]+1,mod-2);
		z[i]=(mod+1-y[i])%mod;
		
		cur=cur+b[i];
		if(x<cur){
			cur=cur+b[i];
		}
		else nx[i]=true;
	}
	if(!nx[1]) return cout << "0\n",0;
	for(int i=1; i<=n ;i++) dpb[1][i]=(pp2[i]-1)*pp2[i]%mod;
	for(int i=2; i<=n ;i++){
		for(int j=1; j<=n-i+1 ;j++){
			if(nx[i]){
				dpb[i][j]=(dpb[i-1][j+1]+(mod-p2[i-1])*dpb[i-1][j])%mod;
				ll dt=((dpb[i-1][j+1]-dps[i-1][j+1]+mod)*z[j]%mod+(mod-p2[i-2])*(dpb[i-1][j]-dps[i-1][j]+mod))%mod;
				dps[i][j]=(dpb[i][j]+mod-dt)%mod;
			}
			else{
				dps[i][j]=(dps[i-1][j+1]+(mod-p2[i-1])*dps[i-1][j])%mod;
				ll dt=((dpb[i-1][j+1]-dps[i-1][j+1]+mod)*y[j]%mod+(mod-p2[i-2])*(dpb[i-1][j]-dps[i-1][j]+mod))%mod;
				dpb[i][j]=(dps[i][j]+dt)%mod;
			}
		}
	}
	/*for(int i=1; i<=n ;i++){
		for(int j=1; j<=n-i+1 ;j++) cout << dps[i][j] << ' ';
		cout << endl;
		for(int j=1; j<=n-i+1 ;j++) cout << dpb[i][j] << ' ';
		cout << endl;
	}*/
	ll ans=dpb[n][1]*(mod+1)/2%mod;//we cannot pick 0
	cout << ans << '\n';
}