#pragma comment(linker, "/STACK:60777216")  

#include <cassert>
#include<iostream>
#include<algorithm>
#include<cstdio>
#include<complex>
#include<vector>
#include<cstring>
#include<set>
#include<map>
#include<cmath>
#include<queue>
#include<string>
#include<cstdlib>
#include<memory.h>
#include<ctime>
#include<bitset>
#include<fstream>
#include<queue>
#include<stack>
#include<unordered_map>
#include<unordered_set>

using namespace std;

typedef long double ld;

typedef long long ll;
typedef pair<int,int>	pii;
typedef pair<ld,ld>	pdd;
typedef vector<int> vi;
typedef vector<ld> vd;
typedef pair<ll,ll> pl;

#define FOR(i,a,b)		for(int i=(a);i<(b);i++)	
#define REP(i,n)		FOR(i,0,n)
#define SORT(v)			sort((v).begin(),(v).end())
#define UN(v)			SORT(v),(v).erase(unique((v).begin(),(v).end()),(v).end())
#define CL(a,b)			memset(a,b,sizeof a)
#define pb				push_back

int n,m,s,k;
int d[111111];
vi  v[111111];

int  res[111111][21][2];
bool   u[111111][21][2];
void solve(){
	CL(res,-1);
	res[s][1][0]=0;
	deque<int> q;
	q.push_back(s*2*21+1*2+0);
	while(!q.empty()){
		int val = q.front();
		q.pop_front();
		int s = val / 2 / 21;
		int e = val % (2 * 21) / 2;
		int a = val % 2;
		//cout<<s<<' '<<e<<' '<<a<<" "<<val<<endl;
		if(u[s][e][a]) continue;
		u[s][e][a]=1;

		int cval = res[s][e][a];

		if(s==0) continue;
		// do nothing
		if(res[d[s]][min(e+1,k)][0]==-1 || res[d[s]][min(e+1,k)][0] > cval){
			res[d[s]][min(e+1,k)][0]=cval;
			q.push_front(d[s]*21*2+min(e+1,k)*2+0);
		}
		// move
		if(e>0)REP(i,v[s].size()){
			if(res[v[s][i]][e-1][1]==-1 || res[v[s][i]][e-1][1] > cval + 1-a){
				res[v[s][i]][e-1][1]=cval + 1-a;
				if(a==1)q.push_front(v[s][i]*21*2+(e-1)*2+1);
				else q.push_back(v[s][i]*21*2+(e-1)*2+1);
			}
		}
	}
}

int main(){	
#ifdef LocalHost
	freopen("input.txt","r",stdin);
	//freopen("output.txt","w",stdout);
#endif
#ifndef LocalHost
	freopen("space.in","r",stdin);
	freopen("space.out","w",stdout);
#endif

	cin>>n>>m>>s>>k;s--;
	REP(i,n-1)scanf("%d",d+i+1),d[i+1]--;
	REP(i,m){
		int x,y;
		scanf("%d %d",&x,&y);
		x--,y--;
		v[x].pb(y);
		v[y].pb(x);
	}
	solve();
	int q;
	cin>>q;
	REP(i,q){
		int x;
		scanf("%d",&x);
		x--;
		int rres = 1e9;
		REP(j,21)if(res[x][j][0]!=-1)rres=min(rres,res[x][j][0]);
		REP(j,21)if(res[x][j][1]!=-1)rres=min(rres,res[x][j][1]);
		if(rres>10000000)rres=-1;
		printf("%d ",rres);
	}
	puts("");

#ifdef LocalHost
	printf("TIME: %.3lf\n",ld(clock())/CLOCKS_PER_SEC);
#endif
	return 0;
}