This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include<iostream>
#include<vector>
#include<algorithm>
#include<queue>
#include<utility>
using namespace std;
typedef long long ll;
int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    int n, m, k, bcnt = 0;
    cin >> n >> m >> k;
    int a, b;
    vector<pair<int, int>> edges;
    for(int i = 1; i <= m; i++){
        cin >> a >> b;
        edges.emplace_back(a, b);
    }
    string s;
    cin >> s;
    vector<bool> isb(n + 1);
    for(int i = 0; i < n; i++){
        if(s[i] == '1'){
            isb[i + 1] = 1;
            bcnt++;
        }
    }
    bcnt++;
    vector<int> vec;
    for(int i = 0; i < k; i++){
        cin >> a;
        vec.push_back(a);
    }
    vector<vector<vector<pair<int, int>>>> graph(n + 1, vector<vector<pair<int, int>>>(bcnt + 1));
    for(auto &[x, y]: edges){
        if(isb[x]){
            for(int i = 0; i < bcnt; i++) graph[y][i].emplace_back(x, i + 1);
        }
        else{
            for(int i = 0; i <= bcnt; i++) graph[y][i].emplace_back(x, i);
        }
        if(isb[y]){
            for(int i = 0; i < bcnt; i++) graph[x][i].emplace_back(y, i + 1);
        }
        else{
            for(int i = 0; i <= bcnt; i++) graph[x][i].emplace_back(y, i);
        }
    }
    vector<vector<int>> dist(n + 1, vector<int>(bcnt + 1, 1e9));
    queue<pair<int, int>> q;
    for(int i = 1; i <= n; i++){
        dist[i][(int)isb[i]] = 0;
        q.emplace(i, (int)isb[i]);
    }
    while(!q.empty()){
        auto [node, cnt] = q.front();
        q.pop();
        for(auto &[v, val]: graph[node][cnt]){
            if(dist[v][val] == 1e9){
                dist[v][val] = dist[node][cnt] + 1;
                q.emplace(v, val);
            }
        }
    }
    vector<vector<int>> dist2(n + 1, vector<int>(bcnt + 1, 1e9));
    dist2[vec[0]][0] = 0;
    q.emplace(vec[0], 0);
    while(!q.empty()){
        auto [node, cnt] = q.front();
        q.pop();
        for(auto &[v, val]: graph[node][cnt]){
            if(dist2[v][val] == 1e9){
                dist2[v][val] = dist2[node][cnt] + 1;
                q.emplace(v, val);
            }
        }
    }
    vector<ll> bans(bcnt + 1);
    for(int i = 0; i < bcnt; i++){
        for(int j = 1; j < k; j++){
            if(isb[vec[j]]){
                bans[i] += 1ll * dist[vec[j]][i + 1];
            }
            else{
                bans[i] += 1ll * dist[vec[j]][i];
            }
        }
    }
    for(int i = 1; i <= n; i++){
        ll ans = 1e18;
        if(i == vec[0]){
            cout << "0\n";
            continue;
        }
        if(isb[i]){
            for(int j = 1; j < bcnt; j++) ans = min(ans, bans[j - 1] + dist2[i][j]);
        }
        else{
            for(int j = 0; j < bcnt; j++) ans = min(ans, bans[j] + dist2[i][j]);
        }
        cout << ans << "\n";
    }
}
// g++ pA.cpp -std=c++17 -Wshadow -Wall -fsanitize=undefined -fsanitize=address -o run 
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