#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define v vector
#define lp(i, s, e) for (ll i = s; i < e; ++i)
ll n, m, k;
v<v<ll>> g;
string s;
v<ll> x;
bool stop(ll u) { return s[u] == '1'; }
const ll inf = 1e18;
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
cin >> n >> m >> k;
g.resize(n + 1);
lp(i, 0, m) {
ll a, b;
cin >> a >> b;
g[a].push_back(b);
g[b].push_back(a);
}
cin >> s;
s = " " + s;
x.resize(k + 1);
lp(i, 1, k + 1) cin >> x[i];
v<ll> sc;
lp(i, 1, n + 1) if (stop(i)) sc.push_back(i);
if (sc.empty()) {
v<ll> d(n + 1, -1);
queue<ll> q;
d[x[1]] = 0;
q.push(x[1]);
while (!q.empty()) {
ll u = q.front();
q.pop();
for (ll w : g[u])
if (d[w] == -1) {
d[w] = d[u] + 1;
q.push(w);
}
}
lp(i, 1, n + 1) cout << d[i] << "\n";
return 0;
}
v<ll> ds(n + 1, inf);
{
queue<ll> q;
for (ll u : sc) {
ds[u] = 0;
q.push(u);
}
while (!q.empty()) {
ll u = q.front();
q.pop();
for (ll w : g[u])
if (ds[w] > ds[u] + 1) {
ds[w] = ds[u] + 1;
q.push(w);
}
}
}
v<ll> pc(n + 1, inf);
lp(i, 1, n + 1) {
ll mn = inf;
for (ll u : g[i])
mn = min(mn, ds[u]);
if (mn != inf)
pc[i] = 1 + mn;
}
v<ll> ns(n + 1, -1);
{
for (ll u : sc)
ns[u] = u;
queue<ll> q;
for (ll u : sc)
q.push(u);
while (!q.empty()) {
ll u = q.front();
q.pop();
for (ll w : g[u])
if (ns[w] == -1) {
ns[w] = ns[u];
q.push(w);
}
}
}
v<ll> ap(n + 1, -1);
lp(i, 1, n + 1) {
ll best = -1, mn = inf;
for (ll u : g[i])
if (ds[u] < mn) {
mn = ds[u];
best = u;
}
if (best != -1)
ap[i] = ns[best];
}
if (k == 2) {
map<tuple<ll, ll, ll>, ll> d;
priority_queue<tuple<ll, ll, ll, ll>, v<tuple<ll, ll, ll, ll>>, greater<>>
pq;
d[{x[1], x[2], 0}] = 0;
pq.push({0, x[1], x[2], 0});
while (!pq.empty()) {
auto [c, p1, p2, t] = pq.top();
pq.pop();
if (d[{p1, p2, t}] < c)
continue;
if (t == 0) {
for (ll w : g[p1]) {
ll nt = stop(w) ? 1 : 0;
auto st = make_tuple(w, p2, nt);
if (!d.count(st) || d[st] > c + 1) {
d[st] = c + 1;
pq.push({c + 1, w, p2, nt});
}
}
} else {
for (ll w : g[p2]) {
ll nt = stop(w) ? 0 : 1;
auto st = make_tuple(p1, w, nt);
if (!d.count(st) || d[st] > c + 1) {
d[st] = c + 1;
pq.push({c + 1, p1, w, nt});
}
}
}
}
lp(i, 1, n + 1) {
ll ans = inf;
for (auto [st, c] : d)
if (get<0>(st) == i)
ans = min(ans, c);
cout << ans << "\n";
}
return 0;
}
v<ll> pos(k + 1);
lp(i, 2, k + 1) pos[i] = x[i];
const ll maxr = 300;
v<ll> rc(maxr);
lp(r, 0, maxr) {
ll c = 0;
lp(i, 2, k + 1) c += pc[pos[i]];
rc[r] = c;
lp(i, 2, k + 1) pos[i] = ap[pos[i]];
}
const ll inf = 1e18;
v<v<array<ll, 2>>> dp(n + 1, v<array<ll, 2>>(maxr, {inf, inf}));
priority_queue<tuple<ll, ll, ll, ll>, v<tuple<ll, ll, ll, ll>>, greater<>> pq;
dp[x[1]][0][0] = 0;
pq.push({0, x[1], 0, 0});
while (!pq.empty()) {
auto [c, u, r, w] = pq.top();
pq.pop();
if (w == 0) {
for (ll v : g[u]) {
ll nw = stop(v) ? 1 : 0;
if (c + 1 < dp[v][r][nw]) {
dp[v][r][nw] = c + 1;
pq.push({c + 1, v, r, nw});
}
}
} else {
if (r < maxr - 1) {
ll nc = c + rc[r];
if (nc < dp[u][r + 1][0]) {
dp[u][r + 1][0] = nc;
pq.push({nc, u, r + 1, 0});
}
}
}
}
lp(i, 1, n + 1) {
ll ans = inf;
lp(r, 0, maxr) {
ans = min(ans, dp[i][r][0]);
ans = min(ans, dp[i][r][1]);
}
cout << ans << '\n';
}
return 0;
}
