#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int MAXN = 50009;
int d1[MAXN], dist[MAXN][5];
pair<int, int> d2[MAXN];
ll add[MAXN];
char stop[MAXN];
vector<int> graph[MAXN];
int main(){
int n, m, K, i, j, a, b;
scanf("%d %d %d", &n, &m, &K);
for(i=0; i<m; i++){
scanf("%d %d", &a, &b);
graph[a].push_back(b);
graph[b].push_back(a);
}
scanf(" %s", stop + 1);
memset(d1, 111, sizeof(d1));
memset(d2, 111, sizeof(d2));
queue<pair<int, int> > qa;
for(i=1; i<=n; i++){
if(stop[i] == '1')
qa.push(make_pair(i, 0));
}
while(!qa.empty()){
auto [v, d] = qa.front();
//printf("v=%d d=%d\n", v, d);
qa.pop();
for(int u: graph[v]){
if(d1[u] > d+1){
d1[u] = d+1;
qa.push(make_pair(u, d1[u]));
}
}
}
deque<int> qb;
for(i=1; i<=n; i++){
if(stop[i] == '1'){
bool flag = 0;
for(int u: graph[i]){
if(stop[u] == '1') flag = 1;
}
if(flag){
qb.push_back(i);
d2[i] = make_pair(0, 0);
}
}
}
while(!qb.empty()){
int v = qb.front();
qb.pop_front();
for(int u: graph[v]){
if(stop[u] == '1'){
pair<int, int> newdist = make_pair(d2[v].first, d2[v].second + 1);
if(newdist < d2[u]){
qb.push_front(u);
d2[u] = newdist;
}
}
else{
pair<int, int> newdist = make_pair(d2[v].first + 1, d2[v].second);
if(newdist < d2[u]){
qb.push_back(u);
d2[u] = newdist;
}
}
}
}
int start;
vector<int> players;
scanf("%d", &start);
for(i=2; i<=K; i++){
int v;
scanf("%d", &v);
players.push_back(v);
}
for(i=1; i<=5; i++){
// printf("i=%d d1=%d d2=(%d,%d)\n", i, d1[i], d2[i].first,d2[i].second);
for(int j: players){
add[i] += min(2*(i-1) + d1[j], i < d2[j].second ? INT_MAX : (d2[j].first + i));
}
//printf("add[%d]=%lld\n",i,add[i]);
}
memset(dist, 111, sizeof(dist));
queue<pair<int, int> > q;
q.push({start, 0});
dist[start][0] = 0;
while(!q.empty()){
auto [v, c] = q.front();
q.pop();
for(int u: graph[v]){
if(stop[u] == '1'){
if(c >= 5) continue;
if(dist[u][c+1] > dist[v][c] + 1){
dist[u][c+1] = dist[v][c] + 1;
q.push({u, c+1});
}
}
else{
if(dist[u][c] > dist[v][c] + 1){
dist[u][c] = dist[v][c] + 1;
q.push({u, c});
}
}
}
}
for(i=1; i<=n; i++){
ll ans = LONG_LONG_MAX;
if(stop[i] == '1'){
for(j=1; j<=5; j++)
ans = min(ans, dist[i][j] + add[j-1]);
}
for(j=0; j<=5; j++){
ans = min(ans, dist[i][j] + add[j]);
}
printf("%lld\n", ans);
}
return 0;
}
