#include <bits/stdc++.h>
using namespace std;
struct trie {
  char ch;
  int son, next, father, suffix;
  vector<int> danger;
  int sum;
};
trie a[205];
int now, m;
void clear(int x) {
  a[x].son = a[x].next = 0;
  a[x].danger.clear();
}
void insert(char *s, int l, int t, int x) {
  if (!a[x].son) {
    a[x].son = ++m;
    clear(m);
    a[m].father = x;
    a[m].ch = s[t];
    if (t + 1 == l)
      a[m].danger.push_back(now);
    else
      insert(s, l, t + 1, m);
    return;
  }
  int i = a[x].son;
  while (1) {
    if (!a[i].next || a[i].ch == s[t]) break;
    i = a[i].next;
  }
  if (a[i].ch == s[t] && t + 1 == l)
    a[i].danger.push_back(now);
  else if (a[i].ch == s[t])
    insert(s, l, t + 1, i);
  else {
    a[i].next = ++m;
    clear(m);
    a[m].father = x;
    a[m].ch = s[t];
    if (t + 1 == l)
      a[m].danger.push_back(now);
    else
      insert(s, l, t + 1, m);
  }
}
int q[205];
int child(int x, char ch) {
  for (int i = a[x].son; i; i = a[i].next)
    if (a[i].ch == ch) return (i);
  if (x == 1) return (1);
  return (child(a[x].suffix, ch));
}
void build_trie() {
  int l, r;
  l = r = 1;
  q[1] = 1;
  while (l <= r) {
    int x = q[l++];
    for (int i = a[x].son; i; i = a[i].next) q[++r] = i;
  }
  a[1].suffix = 1;
  for (int i = 2; i <= r; i++) {
    int x = q[i];
    if (a[x].father == 1) {
      a[x].suffix = 1;
      continue;
    }
    a[x].suffix = child(a[a[x].father].suffix, a[x].ch);
    for (int j = 0; j < (int)a[a[x].suffix].danger.size(); j++)
      a[x].danger.push_back(a[a[x].suffix].danger[j]);
  }
}
int n, base, k;
void read(char *s) {
  int l;
  scanf("%d", &l);
  s[l] = '\0';
  for (int i = 0; i < l; ++i) {
    int a;
    scanf("%d", &a);
    s[i] = a + 'a';
  }
}
int v[205];
char l[205], r[205], s[205];
const int MOD = 1000000007;
int curl;
char cur[205];
int f[205][205][505];
int dp(int i, int state, int sum, bool cmp, bool first) {
  if (sum > k) {
    return 0;
  }
  if (i == 0) {
    return 1;
  }
  if (!first && !cmp && f[i][state][sum] != -1) {
    return f[i][state][sum];
  }
  int ret = 0;
  int r = cur[curl - i] - 'a';
  for (int d = first; d < base; ++d) {
    if (cmp && d > r) {
      continue;
    }
    int nstate = child(state, d + 'a'), nsum = sum + a[nstate].sum;
    bool ncmp = cmp && d == r;
    ret += dp(i - 1, nstate, nsum, ncmp, false);
    if (ret >= MOD) {
      ret -= MOD;
    }
  }
  if (!cmp && !first) {
    f[i][state][sum] = ret;
  }
  return ret;
}
int cal(char *s) {
  int l = strlen(s);
  curl = l;
  for (int i = 0; i < l; ++i) {
    cur[i] = s[i];
  }
  int ret = 0;
  while (curl) {
    ret += dp(curl, 1, 0, curl == l, true);
    --curl;
    if (ret >= MOD) {
      ret -= MOD;
    }
  }
  return ret;
}
int check(char *s) {
  int sum = 0, cur = 1, l = strlen(s);
  for (int i = 0; i < l; ++i) {
    cur = child(cur, s[i]);
    sum += a[cur].sum;
  }
  return sum <= k;
}
int main() {
  memset(f, -1, sizeof(f));
  scanf("%d%d%d", &n, &base, &k);
  read(l), read(r);
  clear(m = 1);
  for (int i = 0; i < n; i++) {
    read(s);
    scanf("%d", v + i);
    now = i;
    insert(s, strlen(s), 0, 1);
  }
  build_trie();
  for (int i = 1; i <= m; ++i) {
    a[i].sum = 0;
    for (int j = 0; j < (int)a[i].danger.size(); ++j) {
      a[i].sum += v[a[i].danger[j]];
    }
  }
  long long ansl = cal(l), ansr = cal(r);
  cout << ((ansr - ansl + check(l)) % MOD + MOD) % MOD << endl;
  return 0;
}
