#include <bits/stdc++.h>
using namespace std;
#define int long long
const int INF = 1e13;
int32_t main(){
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
int n,m,k;
cin >> n >> m >> k;
vector<vector<int>> adj(n+1);
for(int i=1;i<=m;i++){
int u,v;cin>>u>>v;
adj[u].emplace_back(v);
adj[v].emplace_back(u);
}
vector<bool> isStop(n+1);
bool works = false;
for(int i=1;i<=n;i++){
char a;cin>>a;
if(a=='1'){works=isStop[i]=true;}
}
vector<int> starts(k+1);
for(int i=1;i<=k;i++)cin>>starts[i];
vector<int> minmoves(n+1,INF);
minmoves[0]=0;
if(works){
// calculate minmoves
vector<int> nearest_single(n+1,-1);
priority_queue<pair<int,int>> pq;
for(int i=1;i<=n;i++)if(isStop[i])for(int&x:adj[i])pq.emplace(-1,x);
vector<bool> visited(n+1);
while(!pq.empty()){
auto [dist,idx] = pq.top();pq.pop();dist=-dist;
if(visited[idx])continue;
visited[idx]=true;
nearest_single[idx]=dist;
for(int&i:adj[idx])if(!visited[i])pq.emplace(-dist-1,i);
}
vector<int> nearest_double(n+1,-1);
for(int i=1;i<=n;i++)if(isStop[i]){
for(int&x:adj[i]){
if(isStop[x]){
for(int&y:adj[i])pq.emplace(-1,y);
break;
}
}
}
visited = vector<bool>(n+1);
while(!pq.empty()){
auto [dist,idx] = pq.top();pq.pop();dist=-dist;
if(visited[idx])continue;
visited[idx]=true;
nearest_double[idx]=dist;
for(int&i:adj[idx])if(!visited[i])pq.emplace(-dist-1,i);
}
vector<int> slopeedit(n+1);
int base = 0;
auto process = [&](int x){
base+=nearest_single[x];
slopeedit[1]+=2;
if(nearest_double[1]!=-1)slopeedit[nearest_double[x]-nearest_single[x]+1]--;
};
for(int i=2;i<=k;i++){
process(starts[i]);
}
int currslope = 0;
for(int i=1;i<=n;i++){
base+=currslope;
minmoves[i]=base;
currslope+=slopeedit[i];
}
for(int i=n;i;i--)minmoves[i]-=minmoves[i-1];
}
vector<int> currbest(n+1,INF);
vector<int> ans(n+1,INF);
vector<bool> visited(n+1);
priority_queue<tuple<int,int,int>> pq;
pq.emplace(0,0,starts[1]);
while(!pq.empty()){
auto [stops,dist,idx] = pq.top();pq.pop();dist=-dist;stops=-stops;
if(visited[idx])continue;
if(isStop[idx])currbest[idx] = dist-minmoves[stops];
else currbest[idx] = dist;
visited[idx] = true;
for(int&i:adj[idx]){
if(isStop[i]){
if(dist+1+minmoves[stops+1]<currbest[i]){
currbest[i] = dist+1+minmoves[stops+1];
pq.emplace(-stops-1,-dist-1-minmoves[stops+1],i);
visited[i]=false;
} else ans[i]=min(ans[i],dist+1);
} else {
if(dist+1<currbest[i]){
currbest[i] = dist+1;
pq.emplace(-stops,-dist-1,i);
visited[i]=false;
}
}
}
}
for(int i=1;i<=n;i++)cout<<min(currbest[i],ans[i])<<'\n';
}
