#include <iostream>
#include <queue>
#include <vector>
#include <array>
#include <algorithm>
#include <cmath>
#define ll long long
using namespace std;
array<ll, 2> operator+(array<ll, 2> a, array<ll, 2> b) {
return {a[0]+b[0], a[1]+b[1]};
}
queue <ll> Q;
priority_queue <array<ll, 2>, vector<array<ll, 2>>, greater<array<ll, 2>>> pq, U[2];
vector <ll> adj[50000], X;
bool B[50000];
string S;
ll dp[50000][225], mn[50000];
array <ll, 2> stop[50001];
ll n, m, k, a, b, rt, dist[50000], dist2[50000], F[50000], cost[50000];
void search(ll k, ll dlt) {
for (int i=0; i<n; ++i) cost[i] = (ll)1e18, B[i] = 0;
pq.push({0, rt});
cost[rt] = 0;
while (!pq.empty()) {
auto [w, u] = pq.top();
pq.pop();
if (cost[u] != w) continue;
for (auto v : adj[u]) {
if (cost[v] > cost[u] + 1 + (S[v] == '1' ? k : 0)) {
cost[v] = cost[u] + 1 + (S[v] == '1' ? k : 0);
B[v] = B[u] | (S[u] == '1');
pq.push({cost[v], v});
}
}
}
for (int i=0; i<n; ++i) F[i] = min(F[i], cost[i]-(i != rt && S[i] == '1' ? k : 0)-(B[i] ? k : 0)+dlt);
}
int main() {
cin >> n >> m >> k;
for (int i=0; i<m; ++i) {
cin >> a >> b;
--a, --b;
adj[a].push_back(b);
adj[b].push_back(a);
}
cin >> S;
for (int i=0; i<n; ++i) {
dist[i] = F[i] = mn[i] = (ll)1e18;
if (S[i] == '1') Q.push(i), dist[i] = 0;
for (int j=0; j<225; ++j) dp[i][j] = (ll)1e18;
}
while (!Q.empty()) {
auto u = Q.front();
Q.pop();
for (auto v : adj[u]) {
if (dist[v] == (ll)1e18) {
dist[v] = dist[u] + 1;
Q.push(v);
}
}
}
for (int i=0; i<n; ++i) {
dist2[i] = (ll)1e18;
if (S[i] == '1') {
bool ok = 0;
for (auto v : adj[i]) ok |= (S[v] == '1');
if (ok) Q.push(i), dist2[i] = 0;
}
}
while (!Q.empty()) {
auto u = Q.front();
Q.pop();
for (auto v : adj[u]) {
if (dist2[v] == (ll)1e18) {
dist2[v] = dist2[u] + 1;
Q.push(v);
}
}
}
ll s = 0;
for (int i=0; i<n; ++i) {
if (!dist[i]) dist[i] = 2;
if (!dist2[i]) dist2[i] = 1;
}
for (int i=0; i<k; ++i) {
cin >> a;
--a;
if (!i) rt = a;
else X.push_back(a), s += dist[a];
}
S[rt] = '0';
Q.push(rt);
F[rt] = 0;
while (!Q.empty()) {
auto u = Q.front();
Q.pop();
for (auto v : adj[u]) {
if (F[v] > F[u]+1) {
F[v] = F[u]+1;
if (S[v] != '1') Q.push(v);
}
}
}
sort(X.begin(), X.end(), [](auto a, auto b) {
return dist2[a]-dist[a] < dist2[b]-dist[b];
});
if (k <= (ll)sqrt(n)) {
search(2*X.size(), s);
for (int i=0; i<X.size(); ++i) {
s -= dist[X[i]]-dist2[X[i]];
if (dist2[X[i]] == (ll)1e18) break;
search(2*X.size()-i-1, s);
}
}
else {
for (auto u : X) {
stop[max(0LL, dist2[u]-dist[u])] = stop[max(0LL, dist2[u]-dist[u])] + array<ll, 2>{-1, dist2[u]-dist[u]};
}
stop[0] = stop[0] + array<ll, 2>{2*(ll)X.size(), s};
for (int i=1; i<n; ++i) {
stop[i] = stop[i-1] + stop[i];
}
mn[rt] = dp[rt][0] = 0;
U[0].push({0, rt});
for (int t=0; t<n; ++t) {
if (U[0].empty()) break;
while (!U[0].empty()) {
auto [w, u] = U[0].top();
U[0].pop();
if (dp[u][t-mn[u]] != w) break;
for (auto v : adj[u]) {
if (mn[v] == 1e18) mn[v] = t + (S[v] == '1');
if (t+(S[v]=='1')-mn[v] < 225 && dp[v][t+(S[v]=='1')-mn[v]] > w+1) {
dp[v][t+(S[v]=='1')-mn[v]] = w+1;
U[S[v]=='1'].push({w+1, v});
}
}
}
swap(U[0], U[1]);
}
for (int i=0; i<n; ++i) {
for (int j=0; j<225; ++j) {
if (dp[i][j] == (ll)1e18 || (j == 0 && mn[i] == 0)) continue;
ll u = mn[i]+j-1-(S[i] == '1');
if (u < 0) continue;
F[i] = min(F[i], dp[i][j] + u * stop[u][0] + stop[u][1]);
}
}
}
for (int i=0; i<n; ++i) cout << F[i] << '\n';
}
