// what is matter? never mind. 
//#pragma GCC optimize("Ofast")
//#pragma GCC optimize("unroll-loops")
//#pragma GCC target("sse,sse2,sse3,sse4,popcnt,abm,mmx,avx,avx2") 
#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)
#define ll long long
//#define int long long
#define ull unsigned long long
#define SZ(x) ((int)((x).size()))
#define ALL(x) (x).begin(),(x).end()
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 1000000007
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 1005
#define inf 0x3f3f3f3f

#define poly vector<modint>

template<class T>
poly Char(int n,T a){
	static modint f[1005][1005];
	For(i,1,n-1){
		int p=-1;
		For(j,i+1,n)
			if(a[j][i].x){p=j;break;}
		if(p==-1)continue;
		else if(p!=i+1){
			For(j,1,n)swap(a[p][j],a[i+1][j]);
			For(j,1,n)swap(a[j][p],a[j][i+1]);
		}
		For(j,i+2,n){
			modint tmp=a[j][i]/a[i+1][i];
			For(k,1,n)a[j][k]-=tmp*a[i+1][k];
			For(k,1,n)a[k][i+1]+=tmp*a[k][j];
		}
	}
	f[0][0]=1;
	For(i,1,n){
		For(j,0,n)f[i][j]=0;
		For(j,1,i-1){
			modint tmp=a[j][i];
			For(k,j,i-1)tmp*=a[k+1][k];
			For(k,0,i)f[i][k]-=tmp*f[j-1][k];
		}
		For(j,1,n)f[i][j]+=f[i-1][j-1];
		For(j,0,n)f[i][j]-=a[i][i]*f[i-1][j];
	}
	return poly(f[n],f[n]+n+1);
}

template<class T>
modint det(int n,T a){
	modint res=1;
	For(j,1,n){
		For(i,j,n)
			if(a[i][j].x){
				if(i!=j){
					res=-res;
					For(k,i,n)swap(a[i][k],a[j][k]);
				}
				break;
			}
		if(!a[j][j].x)return 0;
		res*=a[j][j];
		modint iv=1/a[j][j];
		For(i,j+1,n){
			modint tmp=a[i][j]*iv;
			For(k,j,n)a[i][k]-=a[j][k]*tmp;
		}
	}
	return res;
}

template<class T>
modint pf(int n,T a){
	modint res=1;
	for(int i=1;i<=n;i+=2){
		if(!a[i][i+1].x){
			int k=i+1;
			while(k<=n && !a[i][k].x)++k;
			if(k>n)return 0;
			swap(a[i][i+1],a[i][k]);
			For(j,k+1,n)swap(a[i+1][j],a[k][j]);
			For(j,i+2,k-1)swap(a[i+1][j],a[j][k]),a[j][k]=-a[j][k],a[i+1][j]=-a[i+1][j];
			a[i+1][k]=-a[i+1][k];
			res=-res;
		}
		res*=a[i][i+1];
		modint I=1/a[i][i+1];
		For(j,i+2,n){
			modint r=a[i][j]*I;
			For(k,j+1,n)a[j][k]-=r*a[i+1][k];
			For(k,i+2,j-1)a[k][j]+=r*a[i+1][k];
		}
	}
	return res;
}

template<class T>
poly detpoly(int n,int d,T a){
	static modint b[1005][1005];
	int out=0;
	modint coe=1;
	For(i,1,n){
		int p=n+1;
		For(re,0,d){
			For(j,1,i-1)if(a[d][j][i].x){
				modint t=a[d][j][i];
				For(e,0,d) For(k,1,n) a[e][k][i]-=a[e][k][j]*t;
			}
			p=i;
			while(p<=n && !a[d][p][i].x)++p;
			if(p<=n || re==d)break;
			++out;
			Rep(e,d,re) For(j,1,n) a[e][j][i]=a[e-1][j][i];
			For(j,1,n) a[0][j][i]=0;
		}
		if(p>n)return poly(n*d+1,0);
		if(p>i){
			coe=-coe;
			For(e,0,d)For(j,1,n)swap(a[e][i][j],a[e][p][j]);
		}
		coe*=a[d][i][i];
		modint I=1/a[d][i][i];
		For(e,0,d)For(j,1,n)a[e][i][j]*=I;
		For(j,i+1,n){
			modint t=a[d][j][i];
			if(t.x){ For(e,0,d) For(k,1,n) a[e][j][k]-=t*a[e][i][k]; }
		}
	}
	For(i,1,n*(d-1))b[i][n+i]=1;
	For(e,0,d-1)For(i,1,n)For(j,1,n)
		b[n*(d-1)+i][n*e+j]=-a[e][i][j];
	poly fs=Char(n*d,b);
	poly f(n*d+1,0);
	For(i,0,n*d-out)f[i]=coe*fs[i+out];
	return f;
}

int n,m,k,a[maxn],b[maxn];
char s[405][405];
modint f[405][405],go[405][405],sum[405][405];
modint mat[3][405][405],g[405][405];
modint res[405];

signed main()
{
	n=read(),m=read(),k=read();
	For(i,1,n)a[i]=read();
	For(i,1,m)b[i]=read();
	For(i,1,k)scanf("%s",s[i]+1);
	
	For(i,1,n){
		memset(f,0,sizeof f);
		f[1][a[i]]=1;
		For(x,1,k)For(y,1,k)
			if(s[x][y]=='1')f[x+1][y]+=f[x][y],f[x][y+1]+=f[x][y];
			else f[x][y]=0;
		For(j,1,m) go[i][j]=f[k][b[j]];
	}
//	if(n%2) ++n,++m,go[n][m]=1;
	For(i,1,n)For(j,1,m)sum[i][j]=sum[i][j-1]+go[i][j];
	For(i,1,n)For(j,i+1,n){
		For(k,1,m){
			modint t=sum[i][k]*go[j][k]-sum[j][k]*go[i][k];
			g[i][j]+=t;
			g[j][i]-=t;
		}
	}
	//For(i,1,n)For(j,1,n)cout<<mat[i][j].x<<" \n"[j==n];
	
	int len=(n%2==0?n+2:n+1);
	For(i,1,len) For(j,i+1,len) {
		mat[0][i][j]+=sign(j-i-1);
		if(i<=n && j<=n) mat[2][i][j]=g[i][j];
	}
	For(i,1,n) mat[1][i][len]=sum[i][n];
	For(d,0,2) For(i,1,len) For(j,i+1,len) mat[d][j][i]=-mat[d][i][j];
	
//	For(d,0,2){
//		For(i,1,len)For(j,1,len)cout<<mat[d][i][j].x<<" \n"[j==len];
//		puts("-----------");
//	}
	poly ans=detpoly(len,2,mat);
	for(auto x:ans)cout<<x.x<<" "; cout<<"\n";
	res[0]=1;
	For(i,1,n){
		res[i]=ans[i];
		For(j,1,i-1)res[i]-=res[j]*res[i-j];
		res[i]*=((mod+1)/2);
	}
	Rep(i,n,0)
		if(res[i].x){
			cout<<i<<" "<<res[i].x<<"\n";
			exit(0);
		}
	return 0;
}
/*

*/