#include<bits/stdc++.h>
#define pb push_back
#define mp make_pair
#define int long long
#define vi vector<int>
#define vvi vector<vector<int>>
#define pii pair<int, int>
#define vpii vector<pair<int, int>>
#define vc vector<char>
#define vb vector<bool>
#define mii map<int,int>
#define f0r(i,n) for(int i=0;i<n;i++)
#define FOR(i,k,n) for(int i=k;i<n;i++)
#define all(v) (v).begin(),(v).end()
#define rall(v) (v).rbegin(),(v).rend()
#define in(a) int a; cin>>a
#define in2(a,b) int a,b; cin>>a>>b
#define in3(a,b,c) int a,b,c; cin>>a>>b>>c
#define in4(a,b,c,d) int a,b,c,d; cin>>a>>b>>c>>d
#define vin(v,n); vi v(n); f0r(i,n){cin>>v[i];}
#define out(a) cout<<a<<'\n'
#define out2(a,b) cout<<a<<' '<<b<<'\n'
#define out3(a,b,c) cout<<a<<' '<<b<<' '<<c<<'\n'
#define out4(a,b,c,d) cout<<a<<' '<<b<<' '<<c<<' '<<d<<'\n'
#define pout(a) cout<<a.first<<' '<<a.second<<'\n'
#define vout(v) for(auto u : v){cout<<u<<' ';} cout<<endl
#define dout(a) cout<<a<<' '<<#a<<endl
#define dout2(a,b) cout<<a<<' '<<#a<<' '<<b<<' '<<#b<<endl
#define yn(x); if(x){cout<<"YES"<<'\n';}else{cout<<"NO"<<'\n';}
const int leg = 1e9 + 7;
const int mod = 998244353;
using namespace std;
const int mxn = 3e3 + 5;
const int mxs = 3e3 + 5;
int N,M,K,scount,X[mxn],dp[mxn][mxs],bs[mxn],gs[mxn],b[mxn],g[mxn],f[mxs],ans[mxn];
string S; vi adj[mxn];
signed main(){
ios::sync_with_stdio(false);
cin.tie(NULL);
cin>>N>>M>>K; f0r(i,M){int a,b; cin>>a>>b; a--;b--; adj[a].pb(b); adj[b].pb(a);} cin>>S; f0r(i,K)cin>>X[i], X[i]--;
f0r(i,N){if(S[i] == '1')b[i] = 1, scount++;}
f0r(i,N){
bs[i] = 4e18; gs[i] = 4e18;
if(b[i])for(auto u : adj[i])if(b[u])g[i] = 1, g[u] = 1;
}
f0r(i,N)if(b[i] && g[i])b[i]=0;
f0r(i,N){
if(b[i])bs[i]=0; else bs[i]=4e18;
if(g[i])gs[i]=0; else gs[i]=4e18;
}
queue<int>q; f0r(i,N)if(b[i])q.push(i);
while(!q.empty()){
int node = q.front(); q.pop();
for(auto u : adj[node]){
if(bs[u] == 4e18)bs[u] = bs[node] + 1, q.push(u);
}
}
f0r(i,N)if(g[i])q.push(i);
while(!q.empty()){
int node = q.front(); q.pop();
for(auto u : adj[node]){
if(gs[u] == 4e18)gs[u] = gs[node] + 1, q.push(u);
}
}
f0r(i,N)if(b[i])bs[i] = 2;
f0r(i,N)f0r(j,scount+1)dp[i][j] = 4e18;
dp[X[0]][0] = 0; queue<pii>qu; qu.push(mp(X[0], 0));
while(!qu.empty()){
int node = qu.front().first; int st = qu.front().second; qu.pop();
// out2(node,st);
// dout(dp[node][st]);
for(auto u : adj[node]){
int nxt = u; int nst = st; if(S[u] == '1')nst++;
if(dp[nxt][nst] == 4e18){
dp[nxt][nst] = dp[node][st] + 1; qu.push(mp(nxt,nst));
// dout2(node, st);
// dout2(nxt,nst);
}
}
}
f[0] = 0;
FOR(i,1,scount+1){
f[i] = 0;
FOR(j,1,K){
// cerr<<X[j]<<' '<<gs[X[j]]<<'\n';
f[i] += min((b[X[j]] != 1) ? bs[X[j]] + 2 * (i-1) : 2 * i, (g[X[j]] != 1) ? gs[X[j]] + (i-1) : i);
}
// cerr<<f[i]<<' ';
}
// cerr<<'\n';
f0r(i,N){
f0r(j, scount+1){
// cout<<dp[i][j]<<' ';
}
// cout<<endl;
}
f0r(i,N){
ans[i] = 4e18;
if(i == X[0])out(0);
else{
f0r(j,scount+1){
// out2(i, j);
if(i == 4){
// dout2(i,j);
// dout(dp[i][j]);
}
ans[i] = min(ans[i], dp[i][j] + f[j-(S[i]-'0')]);
}
cout<<ans[i]<<'\n'; //out("");
}
}
}
