# include <bits/stdc++.h>
# define ll long long
# define ld long double
# define pii pair<int, int>
# define fi first
# define se second
using namespace std;

// complexity : K^2 + 2K * (M log M)

int num[50001], N, M, K;
vector<int> edge[50001];
string S;
bool stop[50001], vis[150011];
ll dist[2][50001], ds[2][50001], ad[3]; // 0 = dist ke yg add 1, 1 dist yg ke add 2
// kalo 1 ada yg dist 0, buat jadi 2
// kalo 0 ada yg dist 0, buat jadi 1

void build() {
	for(int i=1;i<=N;i++) {
		dist[0][i] = dist[1][i] = 1e9;
	}
	priority_queue<pii> PQ;
	for(int i=1;i<=N;i++) {
		if(!stop[i]) continue;
		bool cek = 0;
		for(auto p : edge[i]) {
			if(stop[p]) cek = 1;
		}
		if(cek) PQ.push({0, i});
	}
	for(int i=1;i<=N;i++) vis[i] = 0;
	while(PQ.size()) {
		pii x = PQ.top();
		PQ.pop();
		if(vis[x.se]) continue;
		vis[x.se] = 1;
		dist[0][x.se] = -x.fi;
		
		for(auto p : edge[x.se]) {
			if(!vis[p]) {
				if(!stop[p]) PQ.push({x.fi - 1, p});
				else PQ.push({x.fi, p});
			}
		}
	}
	
	for(int i=1;i<=N;i++) vis[i] = 0;
	for(int i=1;i<=N;i++) {
		if(stop[i]) PQ.push({0, i});
	}
	while(PQ.size()) {
		pii x = PQ.top();
		PQ.pop();
		if(vis[x.se]) continue;
		vis[x.se] = 1;
		if(x.fi <= -1) dist[1][x.se] = -x.fi;
		else dist[1][x.se] = 2;
		
		for(auto p : edge[x.se]) {
			if(!vis[p]) {
				PQ.push({x.fi - 1, p});
			}
		}
	}
	
	for(int i=1;i<=N;i++) {
		if(stop[i]) dist[0][i]++;
	}
	for(int i=2;i<=K;i++) {
		ad[1] += min(dist[0][num[i]], dist[1][num[i]]);
		ad[2] += min(dist[0][num[i]] + 1ll, dist[1][num[i]] + 2ll);
	}
//	cout<<ad[0]<<" "<<ad[1]<<" "<<ad[2]<<endl;
}

ll ans[50001];

int main() {
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	
	cin>>N>>M>>K;
	for(int i=0;i<M;i++) {
		int a, b;
		cin>>a>>b;
		edge[a].push_back(b);
		edge[b].push_back(a);
	}
	
	cin>>S;
	for(int i=0;i<N;i++) {
		stop[i + 1] = S[i] - '0';
	}
	
	for(int i=1;i<=K;i++) cin>>num[i];
	build();
	
	for(int i=1;i<=N;i++) ans[i] = 1e18;
	priority_queue< pair< pair<ll, int>, int> > PQ;
	for(int i=0;i<=3*N;i++) vis[i] = 0;
	PQ.push({{0, 0}, num[1]});
	while(PQ.size()) {
		pair<pair<ll, int>, int> x = PQ.top();
		PQ.pop();
		
	//	cout<<x.se<<" "<<x.fi.se<<endl;
		if(vis[3 * x.se + x.fi.se]) continue;
		vis[3 * x.se + x.fi.se] = 1;
		ans[x.se] = min(ans[x.se], -x.fi.fi + ad[-x.fi.se]);
	//	cout<<"ans : "<<ans[x.se]<<endl;
		for(auto p : edge[x.se]) {
			if(stop[x.se] && x.se != num[1]) {
				int val = x.fi.se - 1;
				if(val > 2) continue;
				if(!vis[3 * p + val]) PQ.push({{x.fi.fi - 1, val}, p});
			} else {
				if(!vis[3 * p + x.fi.se]) PQ.push({{x.fi.fi - 1, x.fi.se}, p});
			}
		}
	}
	for(int i=1;i<=N;i++) cout<<ans[i]<<"\n";
}