//in the name of allah
#include<iostream>
#include<algorithm>
#include<queue>
#include<deque>
#include<set>
#include<map>
#include<bitset>
#include<cstdio>
#include<cstdlib>
#include<cassert>
#include<string>
#include<cstring>
#include<vector>
using namespace std;
typedef pair<int , int> ii;
typedef long long ll;

const int maxn = 3e5+10 , maxm = 2e6+10 , mod = 1e9+7;
vector<int> g[maxn] , r[maxn] , cmp[maxn] , tp;
vector<ii> e;
int n , m , A , B , st[maxn] , len[maxn] , siz[maxn] , d[maxn] , mx[maxn] , mn[maxn] , fact[maxn] , inv[maxn] , sz;
string a[maxn] , b[maxn];
bool vis[maxn];

inline int mul(int a , ll b){
    return (a * b) % mod;
}
inline int add(int a , ll b){
    return (a + b + 2LL*mod) % mod;
}
inline int bp(int a , int b){
    if(b == 0)
        return 1;
    int x = bp(a , b/2);
    x = mul(x , x);
    return b&1 ? mul(x,a) : x;
}
inline int C(int m , int n){
    return n>=m ? mul(fact[n] , mul(inv[m] , inv[n-m])) : 0;
}
void dfs(int v){
    vis[v] = true;
    for(auto u : g[v])
        if(!vis[u])
            dfs(u);
    tp.push_back(v);
}
void sfd(int v){
    vis[v] = true;
    st[v] = sz;
    cmp[sz].push_back(v);
    len[sz] = len[sz] == 0 ? siz[v] : __gcd(len[sz] , siz[v]);
    for(auto u : r[v])
        if(!vis[u])
            sfd(u);
}

int main(){
    scanf("%d%d%d" , &n , &A , &B);
    char STR[maxn];
    for(int i=0 ; i<n ; i++){
        scanf("%s" , STR);
        for(int j=0 ; j<n ; j++){
            if(STR[j] == '1'){
                g[i].push_back(j);
                r[j].push_back(i);
                e.push_back(ii(i , j));
            }
        }
    }
    char str[maxm];
    for(int i=0 ; i<n ; i++){
        scanf("%d%s" , &siz[i] , str);
        mn[i] = 0;
        for(int j=0 ; j<siz[i] ; j++){
            a[i].push_back(str[j]);
            mn[i] += (str[j] == '1');
        }
    }
    if(A<B){
        puts("0");
        return 0;
    }
    for(int i=0 ; i<n ; i++)
        if(!vis[i])
            dfs(i);
    memset(vis , 0 , sizeof vis);
    while((int)tp.size()){
        int i = tp.back();
        tp.pop_back();
        if(!vis[i]){
            sfd(i);
            sz ++;
        }
    }
    for(int i=0 ; i<sz ; i++){
        for(int j=0 ; j<len[i] ; j++)
            b[i] += "0";
        for(auto j : cmp[i])
            for(int k=0 ; k<(int)a[j].size() ; k++)
                b[i][k%len[i]] = char(a[j][k] | b[i][k%len[i]]);
    }
    for(int i=0 ; i<n ; i++)
        g[i].clear();
    for(auto i : e)
        if(st[i.first] != st[i.second])
            g[st[i.first]].push_back(st[i.second]) , d[st[i.second]] ++;
    int cur = -1;
    for(int i=0 ; i<sz ; i++)
        if(d[i] == 0)
            cur = i;
    while(cur != -1){
        int v = cur;
        cur = -1;
        int ptr=0;
        for(auto u : g[v]){
            d[u] --;
            if(d[u] == 0)
                cur = u;
        }
        if(cur == -1)
            break;
        int u = cur;
        int g = __gcd(len[v] , len[u]);
        string str;
        for(int i=0 ; i<g ; i++)
            str += "0";
        for(int i=0 ; i<b[v].size() ; i++)
            str[i%g] = char(b[v][i] | str[i%g]);
        for(int i=0 ; i<b[u].size() ; i++)
            b[u][i] = char(b[u][i] | str[i%g]);
    }
    for(int i=0 ; i<sz ; i++){
        int score=0;
        for(int j=0 ; j<b[i].size() ; j++)
            score += (b[i][j] == '1');
        for(auto j : cmp[i])
            mx[j] = score*(siz[j]/len[i]);
    }
    fact[0] = inv[0] = 1;
    for(int i=1 ; i<=n ; i++){
        fact[i] = mul(i , fact[i-1]);
        inv[i] = bp(fact[i] , mod-2);
    }
    vector<ii > v;
    for(int i=0 ; i<n ; i++){
        v.push_back(ii(mn[i] , 0));
        v.push_back(ii(mx[i] , 1));
    }
    sort(v.begin() , v.end());
    int numa=0 , numb=0 , ans=0;
    for(int i=2*n-1 ; i>=0 ; i--){
        numa += (v[i].second == 0);
        numb += v[i].second;
        if(v[i].second && numb >= B){
            for(int j=0 ; j<=B-1 && j<=numa ; j++){
                int cnt = numa-j;
                if(cnt>A-B)
                    continue;
                ans = add(ans , mul(C(j , numa) , C(B-j-1 , numb-1-numa)));
            }
        }
    }
    printf("%d\n" , ans);
}