#include<bits/stdc++.h>
#define For(i,a,b) for(int i=(a);i<=(b);++i)
#define Rep(i,a,b) for(int i=(a);i>=(b);--i)
using namespace std;
inline int read()
{
	char c=getchar();int x=0;bool f=0;
	for(;!isdigit(c);c=getchar())f^=!(c^45);
	for(;isdigit(c);c=getchar())x=(x<<1)+(x<<3)+(c^48);
	if(f)x=-x;return x;
}

#define mod 998244353
struct modint{
	int x;
	modint(int o=0){x=o;}
	modint &operator = (int o){return x=o,*this;}
	modint &operator +=(modint o){return x=x+o.x>=mod?x+o.x-mod:x+o.x,*this;}
	modint &operator -=(modint o){return x=x-o.x<0?x-o.x+mod:x-o.x,*this;}
	modint &operator *=(modint o){return x=1ll*x*o.x%mod,*this;}
	modint &operator ^=(int b){
		modint a=*this,c=1;
		for(;b;b>>=1,a*=a)if(b&1)c*=a;
		return x=c.x,*this;
	}
	modint &operator /=(modint o){return *this *=o^=mod-2;}
	friend modint operator +(modint a,modint b){return a+=b;}
	friend modint operator -(modint a,modint b){return a-=b;}
	friend modint operator *(modint a,modint b){return a*=b;}
	friend modint operator /(modint a,modint b){return a/=b;}
	friend modint operator ^(modint a,int b){return a^=b;}
	friend bool operator ==(modint a,int b){return a.x==b;}
	friend bool operator !=(modint a,int b){return a.x!=b;}
	bool operator ! () {return !x;}
	modint operator - () {return x?mod-x:0;}
	bool operator <(const modint&b)const{return x<b.x;}
};
inline modint qpow(modint x,int y){return x^y;}

vector<modint> fac,ifac,iv;
inline void initC(int n)
{
	if(iv.empty())fac=ifac=iv=vector<modint>(2,1);
	int m=iv.size(); ++n;
	if(m>=n)return;
	iv.resize(n),fac.resize(n),ifac.resize(n);
	For(i,m,n-1){
		iv[i]=iv[mod%i]*(mod-mod/i);
		fac[i]=fac[i-1]*i,ifac[i]=ifac[i-1]*iv[i];
	}
}
inline modint C(int n,int m){
	if(m<0||n<m)return 0;
	return initC(n),fac[n]*ifac[m]*ifac[n-m];
}
inline modint sign(int n){return (n&1)?(mod-1):(1);}

#define fi first
#define se second
#define pb push_back
#define mkp make_pair
typedef pair<int,int>pii;
typedef vector<int>vi;

#define maxn 2005
#define inf 0x3f3f3f3f

typedef bitset<maxn>bint;

int m,n;
string str;
bint X; 
bint bs[maxn];
void ins(bint x){
	Rep(i,n-1,0)
		if(x[i]){
			if(!bs[i][i])return bs[i]=x,void();
			x^=bs[i];
		}
	puts("0"),exit(0);
}
void gauss(){
	Rep(i,n-1,0)
		For(j,i+1,n-1)
			if(bs[j][i])bs[j]^=bs[i];
}
bool operator <=(bint a,bint b){
	Rep(i,2000,0)
		if(a[i]!=b[i])return a[i]<b[i];
	return 1;
}
void workX(){
	bint now,mx;
	now.reset();
	cin>>str,reverse(str.begin(),str.end());
	For(i,0,n-1)mx[i]=str[i]&1;
	m=0;
//	For(_,0,n-1)cout<<mx[_];puts(" mx");
	Rep(i,n-1,0){
		if(!bs[i][i])continue;
		now^=bs[i];
	//	For(_,0,n-1)cout<<now[_];puts(" now");
		if(now<=mx)X[m]=1;
		else X[m]=0,now^=bs[i];
		++m; 
	}
//	For(i,0,m-1)cout<<X[i];puts("");
	if(!X[0])puts("0"),exit(0);
	n=m;
}

modint f[2005][2005],g[2005][2005];

modint q,pw[maxn],qfac[maxn],qifac[maxn];
void initq(int n){
	pw[0]=qfac[0]=qifac[0]=1;
	For(i,1,n)pw[i]=pw[i-1]*q,qfac[i]=qfac[i-1]*(pw[i]-1),qifac[i]=qifac[i-1]/(pw[i]-1);
}
inline modint qc(int n,int m){
	if(m<0||n<m)return 0;
	return qfac[n]*qifac[m]*qifac[n-m];
}
modint pwpw[2005]; // qpow(2,qpow(2,i))
modint ans[2005];

signed main()
{
	m=read(),n=read();
	For(_,1,m){
		cin>>str,reverse(str.begin(),str.end());
		bint x; x.reset();
		For(i,0,n-1) x[i]=str[i]&1;
		ins(x);
	}
	gauss();
	workX();
	
	q=2,initq(2001);
	pwpw[0]=2;
	For(i,1,n)pwpw[i]=pwpw[i-1]*pwpw[i-1];
	
	// 钦定 n 有 
	modint iv2=(mod+1)/2;
	f[0][0]=1; // has't hit lcp
	g[0][0]=2; // has hit lcp
	
//	For(i,0,n-1)cout<<X[n-1-i];puts(" x");
	
	For(i,0,n-1)
		For(j,0,i){
			if(X[n-1-i]){
				// add one:
				if(i==n-1){
					g[i+1][j+1]+=g[i][j]*pw[i-j]*pwpw[j];
					continue; 
				}
				f[i+1][j+1]+=f[i][j]*pw[i-j];
				g[i+1][j+1]+=g[i][j]*pw[i-j]*pwpw[j];
				// not add one:
				// 1/2 same , 1/2 diff
				// same:
				f[i+1][j]+=f[i][j]*iv2;
				g[i+1][j]+=g[i][j]*iv2;
				// diff:
				f[i+1][j]+=f[i][j]*iv2;
				g[i+1][j]+=f[i][j]*iv2*pwpw[j];
			}else{
				// add one:
				f[i+1][j+1]+=f[i][j]*pw[i-j];
				g[i+1][j+1]+=g[i][j]*pw[i-j];
				// same:
				f[i+1][j]+=f[i][j]*iv2;
				g[i+1][j]+=g[i][j]*iv2;
				// diff:
				f[i+1][j]+=f[i][j]*iv2;
				g[i+1][j]+=f[i][j]*iv2;
			}
		}
//	For(i,0,n){
//		For(j,0,i){
//			cout<<i<<" "<<j<<" "<<f[i][j].x<<' '<<g[i][j].x<<"\n";
//		} 
//	}
//	For(i,1,n) cout<<g[n][i].x<<" \n"[i==n];
	ans[0]=2;
	For(i,1,n) ans[i]=g[n][i]+pwpw[i]*qc(n-1,i);
//	For(i,0,n) cout<<ans[i].x<<" ";puts("");
	modint res=0;
	For(i,0,n) res+=ans[i]*sign(n-i)*qpow(2,1ll*(n-i)*(n-i-1)/2%(mod-1));
	res*=iv2;
	cout<<res.x; 
	return 0;
}
/*
1 1
1
1

2 2
01
10
11
*/