#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <cctype>

#include <iostream>
#include <sstream>
#include <string>

#include <vector>
#include <list>
#include <queue>
#include <set>
#include <map>
#include <stack>
#include <algorithm>
using namespace std;

#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define FOR2(i,a,b) for (int i = (a); i > (b); --i)
/*
#define FOR(i,n) for(int i=0; i < (n); i++)
#define FORD(i,n) for(int i=(n)-1; i >= 0; i--)
#define FORTO(i,a,b) for (int i = (a); i <= (b); ++i)
*/


#define DEBUG(x) cout << '>' << #x << ' ' << x << endl;
#define SIZE(x) int(x.size())

typedef pair<int, int> PII;
typedef long long ll;

void print(const vector<int> & a)
{
	if (a.empty()) printf("0");
	else
	{
		FOR2(i, a.size()-1, -1) printf("%d", a[i]);
	}
}

void add(vector<int> & a, const vector<int> & b)
{
	int carry = 0;
	FOR(i, 0, b.size())
	{
		if (i == a.size()) a.push_back(0);
		a[i] += b[i] + carry;
		carry = a[i] / 10;
		a[i] %= 10;
	}
	int index = b.size();
	while (carry)
	{
		if (index == a.size()) a.push_back(0);
		a[index] += carry;
		carry = a[index] / 10;
		a[index] %= 10;
		++index;
	}
}

int N, L, B, F;
vector<int> graph[1000];
int state[1000];

vector<int> dp[1000][1000];
bool visited[1000][1000];

void go(int node, int len)
{
	if (visited[node][len]) return;
	
	visited[node][len] = true;
	if (state[node] == -1 && len) return;
	if (len == 0)
	{
		//len ak je koncovy
		if (state[node] == -1) dp[node][len].push_back(1);
		return;
	}
	
	FOR(i, 0, graph[node].size())
	{
		go(graph[node][i], len-1);
		add(dp[node][len], dp[graph[node][i]][len-1]);
	}
}

int main()
{
	while (1)
	{
		scanf("%d%d%d%d", &N, &L, &B, &F);
		if (!N) break;
		
		FOR(i, 0, N) graph[i].clear();
		FOR(i, 0, N) state[i] = 0;
		FOR(i, 0, N)
		{
			int node, M, next;
			scanf("%d%d", &node, &M);
			FOR(j, 0, M)
			{
				scanf("%d", &next);
				graph[node-1].push_back(next-1);
			}
		}
		
		int temp;
		FOR(i, 0, B) { scanf("%d", &temp); state[temp-1] = 1; }
		FOR(i, 0, F) { scanf("%d", &temp); state[temp-1] = -1; }
		
		if (L > N) { printf("impossible\n"); continue; } //neda sa
		
		FOR(i, 0, N) FOR(j, 0, L) { visited[i][j] = false; dp[i][j].clear(); }
		vector<int> res;
		FOR(i, 0, N)
			if (state[i] == 1)
			{
				go(i, L-1);
				add(res, dp[i][L-1]);
			}
		if (res.empty())
			printf("impossible\n");
		else
		{
			print(res);
			printf("\n");
		}
	}
	
	return 0;
}