/* 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 = 5000+100, M = 1e5+10, K = 52, MX = 30;
int n, m, k, A[N], dp[N][N], X[N], dp2[N][N];
pii Y[N];
vector<int> g[N];
string s;
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);
}
cin >> s;
s = " " + s;
for(int i = 1; i <= k; ++i){
cin >> A[i];
}
for(int i = 1; i <= n; ++i){
X[i] = MOD;
Y[i] = {MOD, MOD};
}
priority_queue<array<int, 3>> q;
vector<bool> vis(n+1);
for(int i = 1; i <= n; ++i){
if(s[i] == '1'){
X[i] = 0;
q.push({0, 0, i});
}
}
while(!q.empty()){
int v = q.top()[2]; q.pop();
if(vis[v]) continue;
vis[v] = 1;
for(int u: g[v]){
if(X[u] > X[v] + 1){
X[u] = X[v] + 1;
q.push({-X[u], 0, u});
}
}
}
// vis.clear();
// vis.resize(n+1);
// for(int i = 1; i <= n; ++i){
// if(s[i] == '0'){
// for(int j: g[i]){
// if(s[j] == '0'){
// Y[i] = {0, 0};
// }
// }
// if(Y[i].ff == 0) q.push({0, 0, i});
// }
// }
// while(!q.empty()){
// int v = q.top()[2]; q.pop();
// if(vis[v]) continue;
// vis[v] = 1;
// int cost = 1 + (s[v] == '0');
// for(int u: g[v]){
// if(Y[u].ff > Y[v].ff + cost){
// Y[u].ff = Y[v].ff + cost;
// Y[u].ss = Y[v].ss + cost - 1;
// q.push({-Y[u].ff, -Y[u].ss, u});
// }else if(Y[u].ff == Y[v].ff + cost && Y[u].ss > Y[v].ss + cost - 1){
// Y[u].ss = Y[v].ss + cost - 1;
// q.push({-Y[u].ff, -Y[u].ss, u});
// }
// }
// }
for(int i = 0; i <=n ; ++i) for(int j = 0; j <= n; ++j) dp[i][j] = MOD;
dp[A[1]][0] = 0;
for(int j = 0; j <= n; ++j){ // number of zeros
priority_queue<pair<int, int>> Q;
vector<bool> used(n + 5);
for(int i = 1; i <= n; ++i){
Q.push({-dp[i][j], i});
}
while(!Q.empty()){
int v = Q.top().ss;
Q.pop();
if(used[v]) continue;
used[v] = 1;
for(int u: g[v]){
if(s[u] == '1'){
if(dp[v][j] + 1 < dp[u][j + 1]){
dp[u][j + 1] = dp[v][j] + 1;
}
}else{
if(dp[v][j] + 1 < dp[u][j]){
dp[u][j] = dp[v][j] + 1;
Q.push({-dp[u][j], u});
}
}
}
}
// en;
// for(int i = 1; i <= n; ++i){
// cout << dp[i][j] << ' ';
// }
}
for(int i = 0; i <=n ; ++i) for(int j = 0; j <= n; ++j) dp2[i][j] = MOD;
dp2[A[2]][0] = 0;
for(int j = 0; j <= n; ++j){ // number of zeros
priority_queue<pair<int, int>> Q;
vector<bool> used(n + 5);
for(int i = 1; i <= n; ++i){
Q.push({-dp2[i][j], i});
}
while(!Q.empty()){
int v = Q.top().ss;
Q.pop();
if(used[v]) continue;
used[v] = 1;
for(int u: g[v]){
if(s[u] == '1'){
if(dp2[v][j] + 1 < dp2[u][j + 1]){
dp2[u][j + 1] = dp2[v][j] + 1;
}
}else{
if(dp2[v][j] + 1 < dp2[u][j]){
dp2[u][j] = dp2[v][j] + 1;
Q.push({-dp2[u][j], u});
}
}
}
}
}
vector<int> best(n+5);
for(int j = 1; j <= n; ++j){
int cost2 = MOD;
for(int v = 1; v <= n; ++v) cost2 = min(cost2, dp2[v][j]);
best[j] += min(s[A[2]] == '1' ? j * 2 : X[A[2]] + (j-1)*2, cost2);
}
for(int i = 1; i <= n; ++i){
int ans = MOD;
for(int j = 0; j <= n; ++j){
if(s[i] == '1' && j > 0)
ans = min(ans, dp[i][j] + best[j - 1]);
else
ans = min(ans, dp[i][j] + best[j]);
}
cout << ans << '\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();
}
cerr<<"time taken : "<<(float)clock()/CLOCKS_PER_SEC<<" seconds\n";
return 0;
}
