#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define int ll
typedef pair<int,int> pi;
typedef vector <int> vi;
typedef vector <pi> vpi;
typedef pair<pi,ll> pii;
typedef set <ll> si;
typedef long double ld;
#define f first
#define s second
#define FOR(i,s,e) for(int i=s;i<=int(e);++i)
#define DEC(i,s,e) for(int i=s;i>=int(e);--i)
#define pb push_back
#define all(x) (x).begin(), (x).end()
#define lbd(x, y) lower_bound(all(x), y)
#define ubd(x, y) upper_bound(all(x), y)
#define aFOR(i,x) for (auto i: x)
#define mem(x,i) memset(x,i,sizeof x)
#define fast ios_base::sync_with_stdio(false),cin.tie(0)
#define maxn 500010
#define INF int(1e18)
#define MOD 1000000007
#define DEBUG 0
typedef pair <int, pi> ipi;
typedef pair <pi,pi> pipi;
int N,M,K;
vi adj[maxn];
int A[maxn], X[maxn];
int dist1[maxn], dist2[maxn], dist3[maxn],ans[maxn];
void solve(){
cin >> N >> M >> K;
int a,b;
FOR(i,1,M){
cin >> a >> b;
adj[a].pb(b); adj[b].pb(a);
}
string S;
cin >> S;
FOR(i,1,N) A[i] = (S[i-1] == '1');
FOR(i,1,K) cin >> X[i];
FOR(i,1,N) if (A[i]){
aFOR(j, adj[i]) if (A[j]) A[i] = 2;
}
mem(dist1,-1); mem(dist2,-1);
// get distances to stop cell
queue <int> q;
FOR(i,1,N) if (A[i]){
q.push(i); dist1[i] = 0;
}
while (!q.empty()){
int cur = q.front(); q.pop();
aFOR(i, adj[cur]) if (dist1[i] == -1){
dist1[i] = dist1[cur] + 1;
q.push(i);
}
}
// get distances to stop cell pairs (dist - turn no)
deque <int> dq;
FOR(i,1,N) if (A[i] == 2){
dq.pb(i); dist2[i] = 0;
}
while (!dq.empty()){
int cur = dq.front(); dq.pop_front();
aFOR(i, adj[cur]) if (dist2[i] == -1){
dist2[i] = dist2[cur] + (A[cur] == 0);
if (A[cur] == 0) dq.push_back(i);
else dq.push_front(i);
}
}
priority_queue <pi, vector <pi>, greater <pi> > pq;
vpi v;
mem(dist3,-1); FOR(i,1,N) ans[i] = INF;
pq.push(pi(0,X[1]));
dist3[X[1]] = 0;
ans[X[1]] = 0;
vi vect;
FOR(m,0,N/(K-1)+10){
int res = 0;
if (m > 0){
if (dist1[1] == -1) break;
FOR(i,2,K){
int x = X[i];
int val;
if (dist1[x] == 0){
if (dist2[x] == -1) val = 2*m;
else val = min(2*m, m + dist2[x]);
}else{
if (dist2[x] == -1) val = dist1[x] + 2*(m-1);
else val = min(dist1[x] + 2*(m-1), m + dist2[x]);
}
res += val;
}
}
vect.pb(res);
//~ cout << res << ' ';
aFOR(i, v) pq.push(i);
v.clear();
while (!pq.empty()){
pi cur = pq.top(); pq.pop();
if (dist3[cur.s] != cur.f) continue;
aFOR(i, adj[cur.s]) if (dist3[i] == -1 || dist3[i] > cur.f + 1){
dist3[i] = cur.f + 1;
ans[i] = min(ans[i], res + dist3[i]);
if (A[i]) v.pb(pi(dist3[i], i));
else pq.push(pi(dist3[i], i));
}
}
}
FOR(i,0,(int)vect.size()-2){
assert(vect[i+1] - vect[i] >= K - 1);
}
//~ cout << '\n';
FOR(i,1,N){
assert(ans[i] < INF);
cout << ans[i] << '\n';
}
}
int32_t main(){
fast;
solve();
}
