#include <stdio.h>
#include <limits.h>
#define MAX 1010
#define POCET 50
#define MIL 1000000000

struct bigint
{
	int c[POCET];
	int num;
};

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

void set(bigint* a, int val)
{
	a->c[0] = val;
	a->num = 1;
	for (int i = 1; i < POCET; i++)
		a->c[i] = 0;
}

void add(bigint* a, bigint* b)
{
	for (int i = 0; i < b->num; i++)
	{
		a->c[i] += b->c[i];
	}
	if (a->num < b->num)
		a->num = b->num;
	for (int i = 0; i < a->num+1; i++)
	{
		a->c[i+1] += a->c[i] / MIL;
	   	a->c[i] %= MIL;	
	}
	if (a->c[a->num])
		a->num++;	
}

int isnull(bigint* a)
{
	return !(a->num > 1 || a->c[0] != 0);
}

void print(bigint* a)
{
	printf("%d", a->c[a->num-1]);
	for (int i = a->num-2; i >= 0; i--)
		printf("%09d", a->c[i]);
	printf("\n");
}

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++)
			add(&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++)
			{
				set(&pocty[i][j], 0);
			}
		}
		set(&pocty[N+1][0], 1);

		DFS(0);
		if (!isnull(&pocty[0][len+1]))
			print(&pocty[0][len+1]);
		else
			printf("impossible\n");
	}
	return 0;
}