#include<bits/stdc++.h>
using namespace std;
#define int long long
const int N=5e4+10;
int n, m, k, a[N], x[N];
vector<int> g[N];
int d1[N], d2[N];
void bfs2(vector<int> root, int *d, int dd){
for (int i=0; i<=n; ++i) d[i]=1e9;
queue<int> q;
for (int u:root) d[u]=0, q.push(u);
while (q.size()){
int u=q.front(); q.pop();
for (int v:g[u]){
if (d[u] && a[u]) continue;
if (d[v]>=1e9){
d[v]=d[u]+1;
q.emplace(v);
}
}
}
for (int u:root) d[u]=dd;
}
int vis[N];
void bfs3(int root, vector<int> &vv){
queue<int> q;
vis[root]=1; q.push(root);
while (q.size()){
int u=q.front(); q.pop();
vv.push_back(u);
for (int v:g[u]){
if (!vis[v] && a[v]){
vis[v]=1;
q.emplace(v);
}
}
}
}
int f[N][2];
void dijkstra(int root, int sum1, int sum2){
for (int i=0; i<=n; ++i) f[i][0]=f[i][1]=1e18;
priority_queue<pair<int, pair<int, int>>, vector<pair<int, pair<int, int>>>, greater<pair<int, pair<int, int>>>> pq;
pq.push({f[root][0]=0, {root, 0}});
while (pq.size()){
int u=pq.top().second.first, cnt=pq.top().second.second, dist=pq.top().first;
pq.pop();
if (f[u][cnt]!=dist) continue;
if (u!=root && a[u]){
if (!cnt) dist+=sum1;
else dist+=sum2;
cnt=1;
}
for (int v:g[u]){
if (f[v][cnt]>dist+1){
pq.push({f[v][cnt]=dist+1, {v, cnt}});
}
}
}
}
int ans[N];
int32_t main(){
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
cin >> n >> m >> k;
for (int i=1; i<=m; ++i){
int u, v; cin >> u >> v;
g[u].push_back(v);
g[v].push_back(u);
}
string s; cin >> s;
for (int i=1; i<=n; ++i) a[i]=s[i-1]=='1';
for (int i=1; i<=k; ++i) cin >> x[i];
vector<int> v1, v2;
for (int i=1; i<=n; ++i) if (a[i] && !vis[i]){
vector<int> v;
bfs3(i, v);
if ((int)v.size()==1) v1.insert(v1.end(), v.begin(), v.end());
else v2.insert(v2.end(), v.begin(), v.end());
}
bfs2(v1, d1, 2);
bfs2(v2, d2, 1);
memset(ans, 0x3f, sizeof ans);
vector<pair<int, int>> v;
for (int j=2; j<=k; ++j){
v.emplace_back(d1[x[j]], d2[x[j]]);
}
sort(v.begin(), v.end(), [&](pair<int, int> t1, pair<int, int> t2){
return t1.first-t1.second<t2.first-t2.second;
});
for (int i=0; i<=k-1; ++i){
if (v2.empty() && i!=k-1) continue;
if (v1.empty() && i) continue;
int sum1=0, sum2=i*2+(k-1-i);
for (int j=0; j<i; ++j) sum1+=v[j].first;
for (int j=i; j<k-1; ++j) sum1+=v[j].second;
dijkstra(x[1], sum1, sum2);
for (int j=1; j<=n; ++j) ans[j]=min({ans[j], f[j][0], f[j][1]});
}
for (int i=1; i<=n; ++i) cout << ans[i] << '\n';
return 0;
}
