#include<bits/stdc++.h>
using namespace std;
#define endl '\n'
vector<int> dijik(int n,vector<vector<int>> &graph,vector<int> &init){
vector<int> bst(n+1);
priority_queue<pair<int,int>,vector<pair<int,int>>,greater<pair<int,int>>> pq;
for(int i=1;i<=n;i++){
pq.push({init[i],i});
bst[i]=init[i];
}
while(!pq.empty()){
int u=pq.top().second,dist=pq.top().first;
pq.pop();
if(dist>bst[u]){
continue;
}
for(int v:graph[u]){
if(bst[v]>dist+1){
bst[v]=dist+1;
pq.push({bst[v],v});
}
}
}
return bst;
}
signed main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
int n,m,k;
cin >> n >> m >> k;
vector<vector<int>> graph(n+1);
int cnt=0;
int coef=2;
for(int i=0;i<m;i++){
int u,v;
cin >> u >> v;
graph[u].push_back(v);
graph[v].push_back(u);
}
string s;
cin >> s;
s='#'+s;
vector<int> init(n+1);
for(int i=1;i<=n;i++){
init[i]=1e9;
}
for(int i=1;i<=n;i++){
if(s[i]=='1'){
cnt++;
init[i]=0;
}
}
for(int u=1;u<=n;u++){
for(int v:graph[u]){
if(s[u]=='1'&&s[v]=='1'){
coef=1;
}
}
}
int x[k];
vector<int> dist=dijik(n,graph,init);
long long sum=0;
for(int i=0;i<k;i++){
cin >> x[i];
if(i>0){
if(s[x[i]]=='0'){
sum+=dist[x[i]];
}
else{
sum+=coef;
}
}
}
long long ans[n+1];
long long DP[n+1][cnt+1];
for(int i=1;i<=n;i++){
for(int j=0;j<=cnt;j++){
DP[i][j]=1e18;
}
}
DP[x[0]][0]=0;
priority_queue<pair<long long,pair<int,int>>,vector<pair<long long,pair<int,int>>>,greater<pair<long long,pair<int,int>>>> pq;
pq.push({0,{x[0],0}});
while(!pq.empty()){
long long dist=pq.top().first;
int u=pq.top().second.first,c=pq.top().second.second;
pq.pop();
if(dist>DP[u][c]){
continue;
}
for(int v:graph[u]){
if(s[v]=='0'){
if(DP[v][c]>dist+1){
DP[v][c]=dist+1;
pq.push({DP[v][c],{v,c}});
}
}
else if(s[v]=='1'&&c<cnt){
if(DP[v][c+1]>dist+1){
DP[v][c+1]=dist+1;
pq.push({DP[v][c+1],{v,c+1}});
}
}
}
}
for(int i=1;i<=n;i++){
ans[i]=1e18;
if(s[i]=='0'){
ans[i]=min(ans[i],DP[i][0]);
if(cnt>=1){
ans[i]=min(ans[i],DP[i][1]+sum);
}
if(cnt>=2){
ans[i]=min(ans[i],DP[i][2]+sum+coef*(k-1));
}
}
else{
ans[i]=min(ans[i],DP[i][1]);
if(cnt>=2){
ans[i]=min(ans[i],DP[i][2]+sum);
}
}
cout << ans[i] << endl;
}
}
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