#include <stdio.h>
#include <vector>
#include <set>
#include <queue>
#include <map>
using namespace std;

const int MAXD = 50;

struct BigInt {
	char d;
	char c[MAXD];

	void operator += (BigInt& s) {
		static int i, maxd;
		maxd = s.d;
		if (maxd < d) maxd = d;
		for (i = 1; i <= maxd; i++) {
			c[MAXD-i] += s.c[MAXD - i];
			if (c[MAXD-i] > 9) {
				c[MAXD-i] -= 10;
				c[MAXD-i-1]++;
			}
		}
		d = maxd;
		if (c[MAXD -d -1] > 0) d++;
	}
	void zero() {
		static int i;
		for (i = 0; i < MAXD; i++) c[i] = 0;
	}
	bool is_zero() {
		return d == 1 && c[MAXD-d] == 0;
	}
	void one() {
		static int i;
		for (i = 0; i < MAXD; i++) c[i] = 0;
		d = 1;
		c[MAXD - d] = 1;
	}
	void print() {
		static int i;
		for (i = d; i >= 1; i--) printf("%d", c[MAXD-i]);
	}
};

int N, L, B, F, j, k, i, c, t;
set<int> d[1001];
set<int> start, end;
set<int>::iterator it;
queue<pair<int, int> > q;
BigInt m[1001];
BigInt nm[1001];
map<int, long long>::iterator itm;
BigInt ret;

int main() {

	while (scanf("%d%d%d%d", &N, &L, &B, &F), N > 0) {
		start.clear();
		end.clear();
		for (i = 0; i < N; i++) {
			m[i+1].zero();
			scanf("%d%d", &j, &k);
			d[j].clear();
			while (k-- > 0) {
				scanf("%d", &c);
				d[j].insert(c);
			}
		}
		for (i = 0; i < B; i++) {
			scanf("%d", &c);
			start.insert(c);
		}
		for (i = 0; i < F; i++) {
			scanf("%d", &c);
			end.insert(c);
			//printf("e%d\n", c);
		}
		for (it = start.begin(); it != start.end(); ++it) {
			nm[*it].one();
			//q.push(make_pair(1, *it));
		}

		for (k = 1; k < L; k++) {
			bool done = true;
			for (i = 1; i <= N; i++) {
				m[i] = nm[i];
				nm[i].zero();
			}
			for (i = 1; i <= N; i++) {
				if (!m[i].is_zero()) {
					for (it = d[i].begin(); it != d[i].end(); ++it) {
						nm[*it] += m[i];
					}
					done = false;
				}
			}
			if (done) break;
		}

		ret.zero();
		for (i = 1; i <= N; i++) {
			if (end.find(i) != end.end()) ret += nm[i];
		}
		
		if (ret.is_zero()) printf("impossible");
		else ret.print(); putchar('\n');
//		if (ret) printf("impossible\n");
//		else printf("%lld\n", ret);
	}
	return 0;
}