// In the name of Allah
#include <bits/stdc++.h>
using namespace std;
typedef long long int ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef complex<ld> cld;
#define all(x) (x).begin(),(x).end()
#define len(x) ((ll) (x).size())
#define F first
#define S second
#define pb push_back
#define sep ' '
#define endl '\n'
#define Mp make_pair
#define kill(x) cout << x << '\n', exit(0)
#define set_dec(x) cout << fixed << setprecision(x);
#define file_io(x,y) freopen(x, "r", stdin); freopen(y, "w", stdout);
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
const int maxn = 5e4 + 7;
const ll oo = 1e18 + 4;
int n, m, k, vx;
vector<int> adj[maxn];
string s; int M[maxn], Mx[maxn];
int Ax[maxn]; ll D1[maxn], D2[maxn];
ll dis[maxn], disx[maxn]; int mark[maxn];
queue<int> qu; deque<int> dq; vector<int> ls[maxn];
ll ans[maxn];
void pre_bfs() {
while (!qu.empty()) {
int v = qu.front(); qu.pop();
for (int u : adj[v]) {
if (dis[v] + 1 < dis[u]) {
dis[u] = dis[v] + 1;
qu.push(u);
}
}
}
}
void pre_bfsx() {
while (!dq.empty()) {
int v = dq.front(); dq.pop_front();
for (int u : adj[v]) {
int w = 1;
if (M[u] == 1) w = 0;
if (dis[v] + w < dis[u]) {
dis[u] = dis[v] + w;
if (w == 1) dq.pb(u);
else dq.push_front(u);
}
}
}
}
ll getx(ll T) {
if (T == 0) return 0;
ll res = 0;
for (int i = 1; i < k; i++) {
int v = Ax[i];
res += min(D1[v] + 2 * (T - 1), D2[v] + (T - 1));
}
return res;
}
void cal_bfs(int v) {
fill(dis, dis + n, oo); dis[v] = 0;
int W = min(n, ((int) 5e7) / m) + 4;
for (int T = 0; T < W; T++) {
fill(mark, mark + n, 0);
for (int i = 0; i < n; i++) disx[i] = dis[i];
for (int v = 0; v < n; v++) {
if (dis[v] != oo) ls[dis[v]].pb(v);
}
for (int d = 0; d < n; d++) {
for (int v : ls[d]) {
if (mark[v]) continue;
mark[v] = 1;
for (int u : adj[v]) {
if (dis[v] + 1 < dis[u] && !M[u]) {
dis[u] = dis[v] + 1;
ls[dis[u]].pb(u);
}
disx[u] = min(disx[u], dis[v] + 1);
}
}
}
for (int i = 0; i < n; i++) dis[i] = disx[i];
for (int d = 0; d < n; d++) ls[d].clear();
ll Dx = getx(T);
for (int i = 0; i < n; i++) ans[i] = min(ans[i], dis[i] + Dx);
}
}
void solve() {
cin >> n >> m >> k;
for (int i = 0; i < m; i++) {
int u, v;
cin >> u >> v; u--; v--;
adj[u].pb(v); adj[v].pb(u);
}
cin >> s;
for (int i = 0; i < n; i++) M[i] = (s[i] == '1');
for (int i = 0; i < n; i++) {
Mx[i] = 0;
if (!M[i]) continue;
for (int j : adj[i]) {
if (M[j]) {
Mx[i] = 1;
break;
}
}
}
for (int i = 0; i < k; i++) {
cin >> Ax[i]; Ax[i]--;
}
vx = Ax[0];
fill(dis, dis + n, oo);
for (int i = 0; i < n; i++) {
if (M[i]) {
dis[i] = 0; qu.push(i);
}
}
pre_bfs();
for (int i = 0; i < n; i++) {
D1[i] = oo;
for (int j : adj[i]) D1[i] = min(D1[i], dis[j] + 1);
}
fill(dis, dis + n, oo);
for (int i = 0; i < n; i++) {
if (Mx[i]) {
dis[i] = 0; dq.pb(i);
}
}
pre_bfsx();
for (int i = 0; i < n; i++) {
D2[i] = oo;
for (int j : adj[i]) D2[i] = min(D2[i], dis[j] + 1);
}
int t = 0;
for (int i = 0; i < n; i++) t += M[i];
if (t == 0) {
fill(dis, dis + n, oo);
dis[vx] = 0; qu.push(vx);
pre_bfs();
for (int i = 0; i < n; i++) cout << dis[i] << endl;
return ;
}
fill(ans, ans + n, oo);
cal_bfs(vx);
for (int i = 0; i < n; i++) cout << ans[i] << endl;
}
int main() {
ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
int T = 1;
while (T--) {
solve();
}
return 0;
}
