#include<bits/stdc++.h>
#define Gc() getchar()
#define Me(x,y) memset(x,y,sizeof(x))
#define Mc(x,y) memcpy(x,y,sizeof(x))
#define d(x,y) ((m)*(x-1)+(y))
#define R(n) (rnd()%(n)+1)
#define Pc(x) putchar(x)
#define LB lower_bound
#define UB upper_bound
#define fi first
#define se second
#define eb emplace_back
#define all(x) x.begin(),x.end()
using namespace std;using ll=long long;using db=double;using lb=long db;using ui=unsigned;using ull=unsigned long long;using pii=pair<int,int>;
const int N=5e4+5,M=N*4+5,K=1000+5,mod=1e9+7,Mod=mod-1;const db eps=1e-9;const ll INF=5e18+7;mt19937 rnd(28382);
#define Tp template<typename T>
#define Ts template<typename T,typename... Ar>
namespace Debug{
	Tp void _debug(char* f,T t){cerr<<f<<'='<<t<<endl;}
	Ts void _debug(char* f,T x,Ar... y){while(*f!=',') cerr<<*f++;cerr<<'='<<x<<",";_debug(f+1,y...);}
	#ifdef LOCAL
	#define gdb(...) _debug((char*)#__VA_ARGS__,__VA_ARGS__)
	#else 
	#define gdb(...) void()
	#endif
}using namespace Debug;
int n,m,k,X[N],w1[N],w2[N];
vector<int> S[N];
char s[N];
namespace Init{
	int d1[N],d2[N];
	void build(){
		Me(d1,0x3f);
		priority_queue<pii> q;
		for(int i=1;i<=n;i++) if(s[i]=='1') d1[i]=-2,q.emplace(2,i);
		while(!q.empty()){
			auto [w,x]=q.top();w*=-1;q.pop();
			if(w^d1[x]) continue;
			for(int i:S[x]) if(d1[i]>w+1) q.emplace(-(d1[i]=w+1),i);
		}
		Me(d2,0x3f);
		for(int i=1;i<=n;i++) if(s[i]=='1') for(int j:S[i]) if(s[j]=='1'&&d2[i]>0) d2[i]=-1,q.emplace(1,i);
		while(!q.empty()){
			auto [w,x]=q.top();q.pop();w*=-1;
			if(w^d2[x]) continue;
			for(int i:S[x]){
				int v=w+(s[i]^'1');
				if(d2[i]>v) q.emplace(-(d2[i]=v),i);
			}
		}
		// for(int i=1;i<=n;i++) if(d1[i]>=n) gdb(d1[i],d2[i]);
		for(int i=2;i<=k;i++) w1[i]=(d1[X[i]]==-2?0:d1[X[i]]),w2[i]=max(d2[X[i]]+(s[X[i]]=='1'),0);
		// gdb(d1[X[k]],w1[k]);
	}
}
ll ans[N],flag[N];
void build(){
	queue<int> q;
	static int d[N];
	Me(d,0x3f);d[X[1]]=0;q.push(X[1]);
	while(!q.empty()){
		int x=q.front();q.pop();
		if(s[x]=='1'&&x^X[1]) continue;
		for(int i:S[x]) if(d[i]>d[x]+1) d[i]=d[x]+1,q.push(i);
	}
	for(int i=1;i<=n;i++) if(d[i]<=n) ans[i]=d[i],flag[i]=1;
}
namespace Solve1{
	ll f[3005],d[N];
	void Solve(){
		Me(f,0x3f);f[0]=0;
		for(int i=2;i<=k;i++){
			gdb(w1[i],w2[i]);
			for(int j=i;~j;j--) f[j]=min(f[j]+w2[i],(j?f[j-1]:INF)+w1[i]); 
		}
		for(int i=0;i<k;i++){
			Me(d,0x3f);
			// gdb(i,f[i]);
			priority_queue<pair<ll,int> > q;
			d[X[1]]=f[i];q.emplace(-f[i],X[1]);
			while(!q.empty()){
				auto [w,x]=q.top();q.pop();w*=-1;
				if(w^d[x]) continue;
				if(!i) gdb(x,d[x]);
				for(int j:S[x]){
					ll v=w+(s[j]=='1'?i+k-1:0)+1;
					if(d[j]>v) q.emplace(-(d[j]=v),j);
				}
			}
			static ll dw[N];
			Mc(dw,d);Me(d,0x3f);
			for(int j=1;j<=n;j++)if(s[j]=='1'&&j^X[1]){
				for(int h:S[j]) if(s[h]=='0'&&dw[j]+1<d[h]) q.emplace(-(d[h]=dw[j]+1),h);
			}
			while(!q.empty()){
				auto [w,x]=q.top();q.pop();w*=-1;
				if(w^d[x]) continue;
				if(!i) gdb(x,d[x]);
				for(int j:S[x]){
					ll v=w+(s[j]=='1'?i+k-1:0)+1;
					if(d[j]>v) q.emplace(-(d[j]=v),j);
				}
			}
			for(int j=1;j<=n;j++) ans[j]=min(ans[j],d[j]-(s[j]=='1'?i+k-1:0));
			gdb(d[1],flag[1]);
			// if(f[i]<=1e9) gdb(d[585],f[i]);
		}
	}
}
void Solve(){
	scanf("%d%d%d",&n,&m,&k);
	for(int i=1;i<=m;i++){
		int x,y;scanf("%d%d",&x,&y);
		S[x].push_back(y);S[y].push_back(x);
	}
	scanf("%s",s+1);
	for(int i=1;i<=k;i++) scanf("%d",&X[i]);
	Init::build();
	Me(ans,0x3f);
	build();
	if(k<=3000) Solve1::Solve();
	for(int i=1;i<=n;i++) printf("%lld\n",ans[i]);
}
int main(){
	int t=1;
	// scanf("%d",&t);
	while(t--) Solve();
	cerr<<clock()*1.0/CLOCKS_PER_SEC<<'\n';
}