1 #include <queue>
  2 #include <cstring>
  3 #include <cstdio>
  4 using namespace std;
  5 
  6 const int INF=0x3f3f3f3f;
  7 struct AC_auto
  8 {
  9     const static int LetterSize = 26;
 10     const static int TrieSize = LetterSize * ( 1e3 + 50);
 11 
 12     int tot,root,fail[TrieSize],end[TrieSize],next[TrieSize][LetterSize];
 13     int dp[30][150][1<<10];
 14     int newnode(void)
 15     {
 16         memset(next[tot],-1,sizeof(next[tot]));
 17         end[tot] = 0;
 18         return tot++;
 19     }
 20 
 21     void init(void)
 22     {
 23         tot = 0;
 24         root = newnode();
 25     }
 26 
 27     int getidx(char x)
 28     {
 29         return x-‘a‘;
 30     }
 31 
 32     void insert(char *ss,int x)
 33     {
 34         int len = strlen(ss);
 35         int now = root;
 36         for(int i = 0; i < len; i++)
 37         {
 38             int idx = getidx(ss[i]);
 39             if(next[now][idx] == -1)
 40                 next[now][idx] = newnode();
 41             now = next[now][idx];
 42         }
 43         end[now]|=x;
 44     }
 45 
 46     void build(void)
 47     {
 48         queue<int>Q;
 49         fail[root] = root;
 50         for(int i = 0; i < LetterSize; i++)
 51             if(next[root][i] == -1)
 52                 next[root][i] = root;
 53             else
 54                 fail[next[root][i]] = root,Q.push(next[root][i]);
 55         while(Q.size())
 56         {
 57             int now = Q.front();Q.pop();
 58             for(int i = 0; i < LetterSize; i++)
 59             if(next[now][i] == -1)   next[now][i] = next[fail[now]][i];
 60             else
 61             {
 62                  fail[next[now][i]] = next[fail[now]][i];
 63                  end[next[now][i]]|=end[fail[next[now][i]]];
 64                  Q.push(next[now][i]);
 65             }
 66         }
 67     }
 68 
 69     int match(char *ss)
 70     {
 71         int len,now,res;
 72         len = strlen(ss),now = root,res = 0;
 73         for(int i = 0; i < len; i++)
 74         {
 75             int idx = getidx(ss[i]);
 76             int tmp = now = next[now][idx];
 77             while(tmp)
 78             {
 79                 res += end[tmp];
 80                 end[tmp] = 0;//按题目修改
 81                 tmp = fail[tmp];
 82             }
 83         }
 84         return res;
 85     }
 86 
 87     int go(int n,int m,int kd)
 88     {
 89         int ans=0;
 90         memset(dp,0,sizeof dp);
 91         dp[0][0][0]=1;
 92         for(int i=0,mx=1<<m;i<n;i++)
 93         for(int j=0;j<tot;j++)
 94         for(int k=0;k<mx;k++)
 95         for(int p=0;p<LetterSize&&dp[i][j][k];p++)
 96         {
 97             dp[i+1][next[j][p]][k|end[next[j][p]]]+=dp[i][j][k];
 98             if(dp[i+1][next[j][p]][k|end[next[j][p]]]>=20090717)
 99                 dp[i+1][next[j][p]][k|end[next[j][p]]]-=20090717;
100         }
101         for(int i=0,mx=1<<m;i<tot;i++)
102         for(int j=0;j<mx;j++)
103         {
104             int cnt=0;
105             for(int k=0;k<m;k++)
106             if(j&(1<<k))
107                 cnt++;
108             if(cnt>=kd) ans+=dp[n][i][j];
109             if(ans>=20090717) ans-=20090717;
110         }
111         return ans;
112     }
113     void debug()
114     {
115         for(int i = 0;i < tot;i++)
116         {
117             printf("id = %3d,fail = %3d,end = %3d,chi = [",i,fail[i],end[i]);
118             for(int j = 0;j < LetterSize;j++)
119                 printf("%3d",next[i][j]);
120             printf("]\n");
121         }
122     }
123 };
124 AC_auto ac;
125 char ss[2000];
126 int main(void)
127 {
128     int n,k,m;
129     while(~scanf("%d%d%d",&n,&m,&k)&&(m||n||k))
130     {
131         ac.init();
132         for(int i=0;i<m;i++)
133             scanf("%s",ss),ac.insert(ss,1<<i);
134         ac.build();
135         printf("%d\n",ac.go(n,m,k));
136     }
137     return 0;
138 }