/* Author : Mychecksdead */
#include<bits/stdc++.h>
using namespace std;
#define ll long long int
#define MOD (1000000000+7)
#define MOD1 (998244353)
#define pb push_back
#define all(x) x.begin(), x.end()
#define en cout << '\n'
#define ff first
#define ss second
#define pii pair<int,int>
#define vi vector<int>
const int N = 1e6+100, M = 1e5+10, K = 52, MX = 30;
int n, m, k, a[N], is[N];
vi g[N];
ll DP[N];
array<ll, 3> res[N][2]; // 2 dif results for players for 2...k
void solve(){
cin >> n >> m >> k;
for(int i = 1; i <= m; ++i){
int u, v; cin >> u >> v;
g[u].pb(v);
g[v].pb(u);
}
string s; cin >> s;
for(int i = 1; i <= n; ++i){
if(s[i-1] == '0') is[i] = 1;
else is[i] = 0;
}
for(int i = 1; i <= k; ++i){
cin >> a[i];
}
vector<int> dist(n + 1, N);
vector<pii> dist2(n + 1, pii{N, N});
queue<int> q;
priority_queue<array<int, 3>> qq;
for(int i = 1; i <= n; ++i){
if(is[i] == 0){
dist[i] = 0;
q.push(i);
}
}
while(!q.empty()){
int v = q.front(); q.pop();
for(int u: g[v]){
if(dist[u] == N){
dist[u] = dist[v] + 1;
q.push(u);
}
}
}
for(int i = 1; i <= n; ++i){
if(is[i] == 0){
for(int u: g[i]){
if(is[u] == 0){
dist2[i] = {0, 0};
qq.push({0, 0, i});
break;
}
}
}
}
vector<bool> VIS(n + 1);
while(!qq.empty()){
int v = qq.top()[2]; qq.pop();
if(VIS[v]) continue;
VIS[v] = 1;
for(int u: g[v]){
int new_dist = dist2[v].ff + (is[v] == 0 ? 0 : 1);
if(dist2[u].ff > new_dist){
dist2[u] = {new_dist, dist2[v].ss};
if(is[v] == 0){
dist2[u].ss++;
}
qq.push({-dist2[u].ff, -(int)(is[u]), u});
}
}
}
for(int i = 0; i <= n; ++i){
DP[i] = 0;
}
// for(int i = 1; i <= n; ++i){
// cerr << dist2[i].ff << ' ' << dist2[i].ss << '\n';
// }
for(int i = 2; i <= k; ++i){
// first one
res[i][0] = {1, dist[a[i]], 2}; // at first, dist[a[i]], then just +2 +2 +2 +2...
res[i][1] = {dist2[a[i]].ss, dist2[a[i]].ff + dist2[a[i]].ss, 1}; // we will wait for dist2[a[i]].ss phases to take it, then +1 +1 +1 +1...
for(ll j = 1; j <= n; ++j){
// i-th player's contribution to j-th phase, I guess
ll best = MOD;
if(res[i][1][0] == 0){ // if it's already a type-2 cell
best = min(best, j);
}else{
if(res[i][1][0] <= j){ // we need to pass phases
best = min(best, res[i][1][1] + (j - res[i][1][0]));
}
}
if(res[i][0][1] == 0){ // we begin at a stop cell, type-1 cell
best = min(best, j * 2);
}else{
best = min(best, res[i][0][1] + 2 * (j - 1)); // rest
}
DP[j] += best;
// cerr << i << ' ' << j << ' ' << best << '\n';
}
}
priority_queue<array<ll, 3>> Q; // -dist, phase, node
Q.push({0, 0, a[1]});
vector<bool> vis(n + 1);
vector<ll> DIST(n + 1, (ll)(1e18));
DIST[a[1]] = 0;
while(!Q.empty()){
int v = Q.top()[2], phase = Q.top()[1]; Q.pop();
// cerr << v << ' ' << phase << '\n';
if(vis[v]) continue;
vis[v] = 1;
for(int u: g[v]){
ll w = (is[v] == 0 && v != a[1] ? DP[phase + 1] - DP[phase] : 0ll) + 1;
if(!vis[u] && DIST[u] > DIST[v] + w){
DIST[u] = DIST[v] + w;
Q.push({-DIST[u], (is[v] == 0 && v != a[1] ? phase + 1 : phase), u});
}
}
}
// for(int i = 1; i <= n; ++i){
// cerr << i << ": " << DP[i] << '\n';
// }
// en;
for(int i = 1; i <= n; ++i){
cout << DIST[i] << '\n';
}
}
int main(){
cin.tie(0); ios::sync_with_stdio(0);
int tt = 1, aa;
// freopen("in.txt", "r", stdin);
// freopen("out.txt", "w", stdout);
while(tt--){
solve();
en;
}
cerr<<"time taken : "<<(float)clock()/CLOCKS_PER_SEC<<" seconds\n";
return 0;
}
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