#ifndef LOCAL
#pragma GCC Optimize("O3,Ofast,unroll-loops")
#pragma GCC Target("bmi,bmi2,avx,avx2")
#endif
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
#define int ll
#define f first
#define s second
#define mp make_pair
#define pb push_back
#define pii pair<int, int>
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin() (x).rend()
#ifndef LOCAL
#define endl "\n"
#endif
mt19937 rnd(11);
void solve() {
int n, m, k;
cin >> n >> m >> k;
vector<vector<int>> graph(n);
for (int i = 0; i < m; ++i) {
int a, b;
cin >> a >> b;
--a; --b;
graph[a].pb(b);
graph[b].pb(a);
}
string s;
cin >> s;
vector<int> p(k);
for (auto &x : p) {
cin >> x;
--x;
}
int st = p[0];
p.erase(p.begin());
--k;
vector<int> dist1(n, 1e9);
vector<int> dist2(n, 1e9);
vector<int> rd1(n, 1e9);
vector<int> marked(n);
priority_queue<pii> q;
for (int i = 0; i < n; ++i) {
if (s[i] == '1') {
q.push(mp(0, i));
dist1[i] = 0;
}
}
while (!q.empty()) {
int v = q.top().s;
q.pop();
if (marked[v]) {
continue;
}
marked[v] = true;
for (auto &u : graph[v]) {
if (dist1[u] > dist1[v] + 1) {
dist1[u] = dist1[v] + 1;
q.push(mp(-dist1[u], u));
}
}
}
for (int i = 0; i < n; ++i) {
if (s[i] == '1') {
bool ok = false;
for (auto &u : graph[i]) {
if (s[u] == '1') {
rd1[i] = 1;
ok = true;
break;
}
}
if (!ok) {
rd1[i] = 2;
}
} else {
rd1[i] = dist1[i];
}
}
marked.assign(n, false);
for (int i = 0; i < n; ++i) {
if (s[i] == '1') {
bool ok = false;
for (auto &u : graph[i]) {
if (s[u] == '1') {
ok = true;
break;
}
}
if (ok) {
dist2[i] = 0;
q.push(mp(-0, i));
}
}
}
while (!q.empty()) {
int v = q.top().s;
q.pop();
if (marked[v]) {
continue;
}
marked[v] = true;
for (auto &u : graph[v]) {
if (dist2[u] > dist2[v] + (s[v] == '0')) {
dist2[u] = dist2[v] + (s[v] == '0');
q.push(mp(-dist2[u], u));
}
}
}
vector<int> changes;
int y = 0;
for (int i = 0; i < k; ++i) {
y += rd1[p[i]] - 2;
int rd2 = dist2[p[i]] + 1;
if (rd2 != 1e9) {
changes.pb(rd2 - rd1[p[i]] + 1);
}
}
changes.pb(0);
sort(all(changes));
vector<int> ans(n, 1e9);
{
marked.assign(n, false);
vector<int> D(n, 1e9);
D[st] = 0;
q.push(mp(0, st));
ans[st] = 0;
while (!q.empty()) {
int v = q.top().s;
q.pop();
if (marked[v]) {
continue;
}
marked[v] = true;
for (auto &u : graph[v]) {
ans[u] = min(ans[u], D[v] + 1);
if (s[u] == '1') {
continue;
}
if (D[u] > D[v] + 1) {
D[u] = D[v] + 1;
q.push(mp(-D[u], u));
}
}
}
}
int nowk = k * 2 + 1;
int x = 0;
for (int xdi = 0; xdi < changes.size(); ++xdi) {
int xd = changes[xdi];
y += (xd - x) * nowk;
x = xd;
--nowk;
int lb = y - x * nowk;
if (xdi + 1 == changes.size() || changes[xdi + 1] != changes[xdi]) {
marked.assign(n * 2, false);
vector<int> D(n * 2, 1e9);
D[st] = lb;
q.push(mp(0, st));
while (!q.empty()) {
int v_ = q.top().s;
q.pop();
if (marked[v_]) {
continue;
}
marked[v_] = true;
int v = v_ % n;
for (auto u : graph[v]) {
int u_ = u;
if (v_ >= n || s[u] == '1') {
u_ += n;
}
if (v_ >= n) {
ans[u] = min(ans[u], D[v_] + 1);
}
int td = D[v_] + 1;
if (s[u] == '1') {
td += nowk;
ans[u] = min(ans[u], td);
}
if (D[u_] > td) {
D[u_] = td;
q.push(mp(-D[u_], u_));
}
}
}
}
}
for (int i = 0; i < n; ++i) {
cout << ans[i] << endl;
}
}
signed main() {
#ifdef LOCAL
freopen("in.txt", "r", stdin);
freopen("out.txt", "w", stdout);
#else
ios::sync_with_stdio(false);
cin.tie(0);
#endif
int t = 1;
// cin >> t;
while (t--) {
solve();
}
}
