# 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[100011];
ll dist[2][50001], ds[2][50001]; // 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;
		if(x.fi <= -1) dist[0][x.se] = -x.fi;
		else dist[0][x.se] = 1;
		
		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=2;i<=K;i++) {
	//	cout<<"dist : "<<dist[0][num[i]]<<" "<<dist[1][num[i]]<<endl;
		for(int c=0;c<=2*K;c++) ds[1][c] = 1e18;
		for(int c=0;c<=2*K;c++) {
			if(c + 1 <= 2 * K) ds[1][c + 1] = min(ds[1][c + 1], ds[0][c] + dist[0][num[i]]);
			if(c + 2 <= 2 * K) ds[1][c + 2] = min(ds[1][c + 2], ds[0][c] + dist[1][num[i]]);
		}
		for(int c=0;c<=2*K;c++) ds[0][c] = ds[1][c];
	}
}

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;
	for(int i=0;i<=2*K;i++) {
		priority_queue< pair<pair<ll, int>, int> >PQ;
		PQ.push({{0, num[1]}, 0});
		for(int c=1;c<=2 * N + 3;c++) vis[c] = 0;
		while(PQ.size()) {
			pair<pair<ll, int>, int> x = PQ.top();
			PQ.pop();
			if(vis[2 * x.fi.se + x.se]) continue;
		//	if(i == 3) cout<<"here; "<<x.se<<" "<<x.fi.se<<" "<<x.fi.fi<<" "<<ds[0][i]<<" "<<i<<endl;
			ans[x.fi.se] = min(ans[x.fi.se], -x.fi.fi);
			vis[2 * x.fi.se + x.se] = 1;
			
			for(auto p : edge[x.fi.se]) {
			//	if(p == 11) cout<<"go to  11"<<" "<<x.se<<" "<<2 * p + 1<<" "<<vis[2 * p + 1]<<endl;
				if(x.fi.se != num[1] && stop[x.fi.se] && x.se == 0 && !vis[2 * p - 1]) PQ.push({{x.fi.fi - 1ll * ds[0][i] - 1ll, p}, -1});
				else if(x.fi.se != num[1] && stop[x.fi.se] && x.se == -1 && !vis[2 * p - 1]) PQ.push({{x.fi.fi - 1ll * i - 1ll, p}, -1});
				else if((!stop[x.fi.se] || x.fi.se == num[1]) && !vis[2 * p + x.se])PQ.push({{x.fi.fi - 1ll,  p},x.se});
			}
		}
	}
	for(int i=1;i<=N;i++) cout<<ans[i]<<"\n";
}