#include <algorithm>
#include <cstdio>
#include <vector>

using namespace std;

const int mod = 1000000000;

int n, l, b, f;
vector<int> sus[1000];
vector<int> bs;
vector<int> fs;
int res[2][1001][1000];
int len[2][1001];
int cr;
int nt;

void add(int x, int y)
{
    int* a = res[cr][x];
    int* b = res[nt][y];
    int la = len[cr][x];
    int lb = len[nt][y];
    int zv = 0;
    //printf("%d + %d = ", la == 0 ? 0 : a[0], lb == 0 ? 0 : b[0]);
    for (int i = 0; i < min(la, lb); i ++)
    {
        b[i] += a[i] + zv;
        zv = b[i] / mod;
        b[i] %= mod;
    }
    if (la > lb)
    {
        for (int i = lb; i < la; i ++)
        {
            b[i] = a[i] + zv;
            zv = b[i] / mod;
            b[i] %= mod;
        }
        len[nt][y] = la;
    }
    else
    {
        for (int i = la; zv > 0 && i < lb; i ++)
        {
            b[i] += zv;
            zv = b[i] / mod;
            b[i] %= mod;
        }
    }
    if (zv > 0)
    {
        b[len[nt][y]] = zv;
        len[nt][y] += 1;
    }
    //printf("%d\n", b[0]);
}

int main()
{
    scanf("%d %d %d %d", &n, &l, &b, &f);
    while (n > 0)
    {
        for (int i = 0; i < n; i ++)
        {
            sus[i].clear();
        }
        for (int i = 0; i < n; i ++)
        {
            int ii, di;
            scanf("%d %d", &ii, &di);
            ii -= 1;
            for (int j = 0; j < di; j ++)
            {
                int s;
                scanf("%d", &s);
                s -= 1;
                sus[ii].push_back(s);
            }
        }
        bs.clear();
        for (int i = 0; i < b; i ++)
        {
            int bb;
            scanf("%d", &bb);
            bb -= 1;
            bs.push_back(bb);
        }
        fs.clear();
        for (int i = 0; i < f; i ++)
        {
            int ff;
            scanf("%d", &ff);
            ff -= 1;
            fs.push_back(ff);
        }
        //printf("nacitanych %d riadkov\n", n);
        if (l > n)
        {
            printf("impossible\n");
            goto nxt;
        }
        cr = 0;
        for (int i = 0; i < n; i ++)
        {
            len[cr][i] = 0;
        }
        for (int i = 0; i < b; i ++)
        {
            len[cr][bs[i]] = 1;
            res[cr][bs[i]][0] = 1;
        }
        for (int ll = 1; ll < l; ll ++)
        {
            nt = 1 - cr;
            for (int i = 0; i < n; i ++)
            {
                len[nt][i] = 0;
            }
            for (int i = 0; i < n; i ++)
            {
                if (len[cr][i] != 0)
                {
                    for (int j = 0; j < sus[i].size(); j ++)
                    {
                        add(i, sus[i][j]);
                    }
                }
            }
            cr = nt;
        }
        nt = 1 - cr;
        len[nt][1000] = 0;
        for (int i = 0; i < f; i ++)
        {
            add(fs[i], 1000);
        }
        if (len[nt][1000] == 0)
        {
            printf("impossible\n");
            goto nxt;
        }
        else
        {
            printf("%d", res[nt][1000][len[nt][1000] - 1]);
            for (int i = len[nt][1000] - 2; i >= 0; i --)
            {
                printf("%.9d", res[nt][1000][i]);
            }
        }
        printf("\n");
nxt:
        scanf("%d %d %d %d", &n, &l, &b, &f);
    }
    return 0;
}