#include <stdio.h>
#include <limits.h>
#define MAX 1010

int degree[MAX];
long long int pocty[MAX][MAX];
int nasl[MAX][MAX];
int N, z, s, len;

void DFS(int v)
{
	//printf("DFS %d\n", v);
	if (degree[v] == -1)
		return;
	for (int i = 0; i < degree[v]; i++)
	{
		DFS(nasl[v][i]);
		for (int j = 0; j < len+2; j++)
			pocty[v][j+1] += pocty[nasl[v][i]][j];
	}
	
	/*printf("pocty for %d: ", v);
	for (int i = 0; i < 10; i++)
	{
		printf("%lld, ", pocty[v][i]);
	}
	printf("\n");*/

	degree[v] = -1;	
}

int main()
{
	while (1)
	{
		scanf("%d %d %d %d", &N, &len, &z, &s);
		if (N == 0)
			break;
		for (int i = 1; i <= N; i++)
		{
			int deg, deg2;
			scanf("%d %d", &deg2, &deg);
			degree[i] = deg;
			for (int j = 0; j < deg; j++)
			{
				scanf("%d", &nasl[i][j]);
			}			
		}
		degree[0] = z;
		degree[N+1] = 0;
		for (int i = 0; i < z; i++)
		{
			int tmp;
			scanf("%d", &tmp);
			nasl[0][i] = tmp;
		}
		for (int i = 0; i < s; i++)
		{
			int tmp;
			scanf("%d", &tmp);
			nasl[tmp][degree[tmp]++] = N+1;
		}		
		if (len > N)
		{
		   printf("impossible\n");
		   continue;
		}

		for (int i = 0; i < N+5; i++)
		{
			for (int j = 0; j < N+5; j++)
			{
				pocty[i][j] = 0;
			}
		}
		pocty[N+1][0] = 1;

		DFS(0);
		if (pocty[0][len+1])
			printf("%lld\n", pocty[0][len+1]);
		else
			printf("impossible\n");
	}
	return 0;
}