#include <bits/stdc++.h>
#define rep(a,b,c) for(auto a = (b); a != (c); a++)
#define repD(a,b,c) for(auto a = (b); a != (c); a--)
#define repIn(a, b) for(auto& a : (b))
#define repIn2(a, b, c) for(auto& [a, b] : (c))
constexpr bool dbg = 1;
#define DEBUG if constexpr(dbg)
#define DC DEBUG std::cerr
#define eol std::endl
#define ll long long
#define ld long double
#define pb push_back
#define rg ranges
using namespace std;
constexpr int inf = 1e9 + 2;
int n, m, k;
vector<vector<int>> g;
vector<int> isStop;
vector<int> others;
vector<int> dist, closestStop, closestTwo;
vector<vector<int>> skipCostV;
void bfs(vector<int> starts, bool zerStop=0) {
dist.resize(n + 1, inf);
deque<int> q;
repIn(i, starts) q.pb(i), dist[i] = 0;
vector<int> was(n + 1, 0);
while(q.size()) {
auto v = q.front();
q.pop_front();
if(was[v]) continue;
was[v] = 1;
repIn(u, g[v]) {
if(zerStop && isStop[u]) {
if(dist[u] > dist[v]) dist[u] = dist[v], q.push_front(u);
}
else if(dist[u] > dist[v] + 1) dist[u] = dist[v] + 1, q.pb(u);
}
}
}
int32_t main() {
ios_base::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr);
cin >> n >> m >> k;
g.resize(n + 1);
isStop.resize(n + 1);
rep(i, 0, m) {
int a, b;
cin >> a >> b;
g[a].pb(b);
g[b].pb(a);
}
char c;
rep(i, 1, n + 1) cin >> c, isStop[i] = c == '1';
k--;
others.resize(k);
int start;
cin >> start;
rep(i, 0, k) cin >> others[i];
vector<int> V;
rep(i, 1, n + 1) if(isStop[i]) V.pb(i);
bfs(V);
swap(dist, closestStop);
V.clear();
rep(v, 1, n + 1) if(isStop[v]) repIn(u, g[v]) if(isStop[u] && u > v) V.pb(v), V.pb(u);
bfs(V, 1);
swap(dist, closestTwo);
int cntStop = 0;
rep(v, 1, n + 1) cntStop += isStop[v];
skipCostV.resize(n + 1, vector<int>(cntStop + 1));
rep(v, 1, n + 1) rep(i, 1, cntStop + 1) { skipCostV[v][i] = min(closestStop[v] + 2 * (i - !isStop[v]), closestTwo[v] + i - !isStop[v]); }
vector<int> skipCost(cntStop + 1);
rep(i, 0, cntStop + 1) repIn(v, others) skipCost[i] += skipCostV[v][i];
vector<vector<int>> ans(n + 1, vector<int>(cntStop + 2, inf));
ans[start][0] = 0;
queue<int> q, q2;
q.push(start);
int lvl = 0;
while(q.size() && lvl <= cntStop) {
auto v = q.front();
q.pop();
auto d = ans[v][lvl];
repIn(u, g[v]) if(ans[u][lvl + isStop[u]] > d + 1) ans[u][lvl + isStop[u]] = d + 1, (isStop[u] ? q2 : q).push(u);
if(q.empty()) swap(q, q2), lvl++;
}
rep(i, 1, n + 1) rep(j, 1, cntStop + 1) ans[i][j] += skipCost[j - (isStop[i])];
rep(i, 1, n + 1) {
int mn = ans[i][0];
rep(j, 0, cntStop + 1) mn = min(mn, ans[i][j]);
cout << mn << '\n';
}
}
