#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define int ll
const int inf = 2e15;
using pii = pair<int, int>;
#define fr first
#define sc second
signed main() {
ios_base::sync_with_stdio(false);
cin.tie(0);
int n, m, k;
cin >> n >> m >> k;
vector<vector<int>> vec(n);
vector<bool> stop(n);
for (int i = 0; i < m; i ++) {
int u, v;
cin >> u >> v;
u --, v --;
vec[u].push_back(v);
vec[v].push_back(u);
}
int nrStop = 0;
for (int i = 0; i < n; i ++) {
char ch;
cin >> ch;
stop[i] = ch - '0';
nrStop += stop[i];
}
vector<int> start(k);
for (int i = 0; i < k; i ++) {
cin >> start[i];
start[i] --;
}
vector<int> distStart(n, inf), dp(n, 0);
distStart[start[0]] = 0;
queue<int> st;
st.push(start[0]);
vector<bool> viz(n, false);
while (!st.empty()) {
int x = st.front();
st.pop();
if ((x != start[0] && stop[x]) || viz[x])
continue;
viz[x] = true;
for (auto i : vec[x]) {
distStart[i] = min(distStart[i], 1 + distStart[x]);
st.push(i);
}
}
vector<int> ans(n, inf);
for (int rep = 0; rep <= nrStop; rep ++) {
int sum = 0;
for (int i = 1; i < k; i ++) {
sum += dp[start[i]];
}
for (int i = 0; i < n; i ++)
ans[i] = min(ans[i], distStart[i] + sum);
//recalc distStart
auto distStart2 = distStart;
priority_queue<pii> pq;
for (int i = 0; i < n; i ++)
pq.push({-distStart[i], i});
viz.assign(n, 0);
while (!pq.empty()) {
auto x = pq.top();
pq.pop();
if (viz[x.sc])
continue;
viz[x.sc] = true;
x.fr *= -1;
distStart2[x.sc] = x.fr;
for (auto i : vec[x.sc]) {
int nw = 1;
if (stop[x.sc])
nw += distStart[x.sc];
else
nw += distStart2[x.sc];
if (distStart2[i] > nw) {
distStart2[i] = nw;
pq.push({-nw, i});
}
}
}
distStart = distStart2;
//recalc dp
if (rep == 0)
for (int i = 0; i < n; i ++)
if (!stop[i])
dp[i] = inf;
vector<int> dp2(n, inf);
for (int i = 0; i < n; i ++) {
if (!stop[i])
continue;
for (auto j : vec[i])
pq.push({-dp[i] - 1, j});
}
viz.assign(n, 0);
while (!pq.empty()) {
auto x = pq.top();
pq.pop();
if (viz[x.sc])
continue;
viz[x.sc] = true;
x.fr *= -1;
dp2[x.sc] = x.fr;
if (!stop[x.sc]) {
for (auto i : vec[x.sc]) {
int nw = x.fr + 1;
if (dp2[i] > nw) {
dp2[i] = nw;
pq.push({-nw, i});
}
}
}
}
dp = dp2;
}
for (int i = 0; i < n; i ++)
cout << ans[i] << '\n';
}
/*
imi trebuie un dp de tipul: pentru fiecare casuta stii numarul minim de operatii tipul 1 necesar
acum tu poti veni de la oricare alta casuta pe o ruta fara stop-uri
*/
