#include <bits/stdc++.h>
#define ll long long
#define int ll
using namespace std;
const int mxN = 5e4+5;
int n, m, k, a[mxN], st[mxN];
vector <int> adj[mxN];
string s;
int32_t main() {
ios::sync_with_stdio(0), cin.tie(0);
cin >> n >> m >> k;
for (int i = 0, u, v; i < m; i++) {
cin >> u >> v;
adj[u].emplace_back(v);
adj[v].emplace_back(u);
}
cin >> s;
for (int i = 0; i < n; i++) a[i+1] = s[i] - '0';
for (int i = 1; i <= k; i++) cin >> st[i];
vector <int> ST;
for (int i = 1; i <= n; i++) if (a[i]) ST.emplace_back(i);
auto bfs = [&] (int x, vector <int> &dis) {
queue <int> q;
q.emplace(x);
dis[x] = 0;
while (q.size()) {
int u = q.front(); q.pop();
for (auto v : adj[u]) if (dis[v] > dis[u] + 1) dis[v] = dis[u] + 1, q.emplace(v);
}
};
if (ST.empty()) {
vector <int> dis(n+1, INT_MAX);
bfs(st[1], dis);
for (int i = 1; i <= n; i++) cout << dis[i] << '\n';
exit(0);
} else if ((int) ST.size() == 1) {
vector <int> dx(n+1, INT_MAX);
bfs(ST[0], dx);
ll cst = 0;
for (int i = 2; i <= k; i++) cst += (dx[st[i]] == 0 ? 2 : dx[st[i]]);
priority_queue <pair <ll, int>> q;
vector <int> dis(n+1, INT_MAX);
dis[st[1]] = 0;
q.emplace(0, st[1]);
while (q.size()) {
auto [w, u] = q.top();
q.pop(); w = -w;
if (dis[u] != w) continue;
if (u != st[1] && a[u]) w += cst;
for (auto v : adj[u]) {
if (dis[v] > w + 1) q.emplace(-(dis[v] = w + 1), v);
}
}
for (int i = 1; i <= n; i++) cout << dis[i] << '\n';
exit(0);
} else if ((int) ST.size() == 2) {
vector <int> dx1(n+1, INT_MAX), dx2(n+1, INT_MAX);
bfs(ST[0], dx1);
bfs(ST[1], dx2);
ll cst = 0;
for (int i = 2; i <= k; i++) {
cst += min((dx1[st[i]] == 0 ? 2 : dx1[st[i]]), (dx2[st[i]] == 0 ? 2 : dx2[st[i]]));;
}
priority_queue <tuple <ll, int, int>> q;
vector <vector <ll>> dis(n+1, vector <ll>(3, LLONG_MAX));
dis[st[1]][0] = 0;
q.emplace(0, 0, st[1]);
while (q.size()) {
auto [w, c, u] = q.top();
q.pop(); w = -w;
if (dis[u][c] != w) continue;
if (u != st[1] && a[u]) {
if (c == 0) c++, w += cst;
else c++, w += min(2LL, dx1[ST[1]]) * (k - 1);
}
if (c > 2) continue;
for (auto v : adj[u]) {
if (dis[v][c] > w + 1) q.emplace(-(dis[v][c] = w + 1), c, v);
}
}
for (int i = 1; i <= n; i++) cout << min({dis[i][0], dis[i][1], dis[i][2]}) << '\n';
exit(0);
}
vector <int> OK, kk(n+1);
for (auto &u : ST) for (auto &v : adj[u]) if (a[v]) { kk[u] = 1, OK.emplace_back(u); break; }
if (OK.empty()) {
priority_queue <tuple <ll, int, int>> q;
vector <ll> dis(n+1, LLONG_MAX);
for (auto &e : ST) dis[e] = 0, q.emplace(0, 0, e);
while (q.size()) {
auto [w, c, u] = q.top(); q.pop();
w = -w;
if (dis[u] != w) continue;
for (auto v : adj[u]) {
if (dis[v] > w + 1) q.emplace(-(dis[v] = w+1), 0, v);
}
}
vector <ll> dp(n+1, 0);
for (int i = 2; i <= k; i++) {
ll b = dis[st[i]], mn = LLONG_MAX;
if (b == 0) b = 2 - kk[st[i]];
assert(b < LLONG_MAX); // --> RTE
for (int j = 1; j <= n; j++) {
dp[j] += min(b + 2 * (j-1), (mn == LLONG_MAX ? LLONG_MAX : mn + j));
}
// if (i == 2) cout << '\n';
}
// for (int i = 1; i <= n; i++) cout << dp[i] << ' '; cout << '\n';
vector <vector <pair <ll, ll>>> D(n+1, vector <pair <ll, ll>> (2, make_pair(LLONG_MAX, LLONG_MAX)));
q.emplace(0, 0, st[1]);
D[st[1]][0] = make_pair(0, 0);
while (q.size()) {
auto [w, c, u] = q.top(); q.pop();
w = -w;
int C = (c > 0);
if (D[u][C] != make_pair(w, c)) continue;
if (u != st[1] && a[u]) C = 1, c++, w += dp[c] - dp[c-1];
if (c > n) continue;
for (auto v : adj[u]) {
if (D[v][C].first > w + 1) {
q.emplace(-(D[v][C] = make_pair(w + 1, c)).first, c, v);
} else if (D[v][C].first == w+1 && C && D[v][C].second < c) {
q.emplace(-(D[v][C] = make_pair(w + 1, c)).first, c, v);
}
}
}
for (int i = 1; i <= n; i++) {
ll ans = min(D[i][0].first, D[i][1].first);
assert(ans < LLONG_MAX);
cout << ans << '\n';
}
return 0;
}
priority_queue <tuple <ll, int, int>> q;
vector <ll> dis(n+1, LLONG_MAX);
for (auto &e : ST) q.emplace(0, 0, e);
while (q.size()) {
auto [w, c, u] = q.top(); q.pop();
w = -w;
if (w > 0 && dis[u] != w) continue;
for (auto v : adj[u]) {
if (dis[v] > w + 1) q.emplace(-(dis[v] = w+1), 0, v);
}
}
vector <ll> dx(n+1, LLONG_MAX);
for (auto &e : OK) dx[e] = 0, q.emplace(0, 0, e);
while (q.size()) {
auto [w, c, u] = q.top(); q.pop();
w = -w;
if (dx[u] != w) continue;
w -= a[u];
for (auto v : adj[u]) {
ll nw = w + 1;
if (dx[v] > nw) q.emplace(-(dx[v] = nw), 0, v);
}
}
vector <ll> dp(n+1, 0), dp2(n+1, 0), DP(n+1, 0);
for (int i = 2; i <= k; i++) {
ll b = dis[st[i]], c = dx[st[i]];
// find k such that
// b + 2 * (k - 1) > c + k
// b + 2 * k - 2 > c + k
// k > c - b + 2
ll id = c - b + 2 + 1;
// BRUTEFORCE
// cout << b << ' ' << c << '\n';
// cout << id << '\n';
// continue;
id = max(id, 1LL);
if (id > n) {
dp[1] += b - 2;
dp2[1] += 2;
} else {
dp[1] += b - 2;
dp2[1] += 2;
dp[id] -= b - 2;
dp2[id] -= 2;
dp[id] += c;
dp2[id] += 1;
}
// for (int j = 1; j < id && j <= n; j++) dp[j] += b + 2 * (j - 1);
// for (int j = id; j <= n; j++) dp[j] += c + j;
}
ll cnt = 0;
for (int i = 1; i <= n; i++) {
dp[i] += dp[i-1];
cnt += dp2[i];
DP[i] = dp[i] + cnt * i;
}
vector <vector <pair <ll, ll>>> D(n+1, vector <pair <ll, ll>> (2, make_pair(LLONG_MAX, LLONG_MAX)));
q.emplace(0, 0, st[1]);
D[st[1]][0] = make_pair(0, 0);
while (q.size()) {
auto [w, c, u] = q.top(); q.pop();
w = -w;
int C = (c > 0);
if (D[u][C] != make_pair(w, c)) continue;
if (u != st[1] && a[u]) C = 1, c++, w += DP[c] - DP[c-1];
if (c > n) continue;
for (auto v : adj[u]) {
if (D[v][C].first > w + 1) {
q.emplace(-(D[v][C] = make_pair(w + 1, c)).first, c, v);
} else if (D[v][C].first == w+1 && C && D[v][C].second < c) {
q.emplace(-(D[v][C] = make_pair(w + 1, c)).first, c, v);
}
}
}
for (int i = 1; i <= n; i++) {
ll ans = min(D[i][0].first, D[i][1].first);
assert(ans < LLONG_MAX);
cout << ans << '\n';
}
}
