#include <stdio.h>

#include <set>
#include <vector>

using namespace std;

int n, l, b, f;

#define DEBUG(a)

vector<int> graf[2000];

const int ciflen = 1000000000;

struct L
{
	int len;
	int cif[100];

	void print() const
	{
		for (int i = len-1; i >= 0; i--)
		{
			printf("%d", cif[i]);
		}
		printf("\n");
	}

	void operator = (int a)
	{
		len = 1;
		cif[0] = a;
	}

	/*
	void operator += (int a)
	{
		cif[0] += a;
		int pos = 0;
		while (pos < len && cif[pos] > ciflen)
		{
			cif[pos] -= ciflen;
			cif[++pos]++;
		}
		if (cif[len-1] > ciflen)
		{
			len++;
			cif[len-1] = 1;
		}
	}
	*/

	void operator += (const L &a)
	{
		if (len < a.len) len = a.len;
		bool carry = false;
		for (int i = 0; i < len; i++)
		{
			cif[i] += a.cif[i];
			if (carry) cif[i] += 1;
			carry = false;
			if (cif[i] >= ciflen)
			{
				carry = true;
				cif[i] -= ciflen;
			}
		}
		if (carry)
		{
			len++;
			cif[len-1] = 1;
		}
	}

	L()
	{
		len = 1;
		for (int i = 0; i < 100; i++) cif[i] = 0;
	}
};

struct V
{
	int vrchol;
	L nasob;
};

bool operator == (const V &a, const V &b)
{
	return a.vrchol == b.vrchol;
}

bool operator < (const V &a, const V &b)
{
	return a.vrchol < b.vrchol;
}

bool operator <= (const V &a, const V &b)
{
	return a.vrchol <= b.vrchol;
}


int main()
{
/*
	L xxx, yyy;
	xxx = 999999;
	yyy = 999999;

	xxx += yyy;
	xxx.print();
*/

	scanf("%d %d %d %d\n",&n,&l,&b,&f);

	while (n >0 && l > 0 && b > 0 && f > 0)
	{
		for (int i = 1; i < n+1; i++)
		{
			graf[i].clear();

			int cv, ps, vrch;
			scanf("%d %d", &cv, &ps);
			for (int j = 0; j < ps; j++)
			{
				scanf("%d", &vrch);
				graf[cv].push_back(vrch);
				DEBUG( printf("cesta z %d do %d\n", cv , vrch); )
			}
		}

		for (int i = 0; i < b; i++)
		{
			int start;
			scanf("%d", &start);
			graf[n+1].push_back(start);
		}

		for (int i = 0; i < f; i++)
		{
			int konec;
			scanf("%d", &konec);
			graf[konec].push_back(n+2);
		}

		// cool :-)

		if (l > n) printf("impossible\n");
		else
{
	// CVUTaci neumi nakonfigurit vim

	V pocatek;
	pocatek.vrchol = n+1;
	pocatek.nasob = 1;

	set<V> vrstva;
	set<V> nasled;

	vrstva.insert(pocatek);
	
	for (int i = 0; i < l+1; i++)
	{
		for (set<V>::iterator it = vrstva.begin(); it != vrstva.end(); ++it)
		{
			for (vector<int>::iterator it2 = graf[(*it).vrchol].begin(); it2 != graf[(*it).vrchol].end(); ++it2)
			{
				V vyhledavatko;
				vyhledavatko.vrchol = (*it2);
				set<V>::iterator f = nasled.find(vyhledavatko);
				if (f == nasled.end())
				{
					V novy;
					novy.vrchol = (*it2);
					novy.nasob = (*it).nasob;
					nasled.insert(novy);
				} else
				{
					V tmp = (*f);
					nasled.erase(f);
					tmp.nasob += (*it).nasob;
					nasled.insert(tmp);
					//(*f).nasob += (*it).nasob;
				}
			}
		}

		vrstva = nasled;
		nasled.clear();

		DEBUG(
		printf("vrstva %d: \n", i);
		for (set<V>::iterator it = vrstva.begin(); it != vrstva.end(); ++it)
		{
			printf("  %d (%d)\n", (*it).vrchol, (*it).nasob);
		}
		)
	}
	
	V koncovych;
	koncovych.vrchol = n+2;
	set<V>::iterator f = vrstva.find(koncovych);
	if (f != vrstva.end()) (*f).nasob.print(); else printf("impossible\n");
}

		

		scanf("%d %d %d %d\n",&n,&l,&b,&f);
	}


	return 0;
}