#include<bits/stdc++.h>
#define poly vector<int>
#define IOS ios::sync_with_stdio(false)
#define ll long long
#define mp make_pair
#define mt make_tuple
#define pa pair < int,int >
#define fi first
#define se second
#define inf 1e18
#define mod 998244353
#define sz(x) (int)((x).size())
#define int ll
//#define N
using namespace std;
const int N=50005;
int n,m,K;
int ss[N];
int ds[N];
poly G[N];
int vis[N];
int vs[N];
int dis[N],dis1[N],tot[N];
int X[N];
int fuck[N];
int coef;
int s[N];
int ans[N];
int f[N][1005];
const int B=250;
void BellaKira()
{
	cin>>n>>m>>K;
	for (int i=1;i<=m;i++)
	{
		int x,y;
		cin>>x>>y;
		G[x].push_back(y);
		G[y].push_back(x);
	}
	for (int i=1;i<=n;i++)
	{
		char c;
		cin>>c;
		if (c=='0')
			vis[i]=0;
		else vis[i]=1;
	}
	for (int i=1;i<=K;i++)
		cin>>X[i];
	{
		queue<int>q;
		for (int i=1;i<=n;i++) dis[i]=inf;
		for (int i=1;i<=n;i++)
		{
			for (auto u:G[i])
				if (vis[u])
					dis[i]=1,q.push(i);
		}
		while (!q.empty())
		{
			int u=q.front();
			q.pop();
			for (auto v:G[u])
				if (dis[v]>dis[u]+1)
				{
					q.push(v);
					dis[v]=dis[u]+1;
				}
		}
		for (int i=1;i<=n;i++) dis1[i]=inf,tot[i]=0,vs[i]=0;
		for (int i=1;i<=n;i++)
			for (auto u:G[i])
				if (vis[u]==1&&vis[i]==1) fuck[i]=1;
		{
			priority_queue<pa>q;
			for (int i=1;i<=n;i++)
			{
				for (auto u:G[i])
					if (fuck[u])
					{
						dis1[i]=1;
						tot[i]=1;
						q.push(mp(-dis1[i],i));
					}
			}
			while (!q.empty())
			{
				auto [w,u]=q.top();
				q.pop();
				w=-w;
				if (w!=dis1[u]) continue;
				for (auto v:G[u])
				{
					if (dis1[v]>dis1[u]+(vis[u]^1))
					{
						dis1[v]=dis1[u]+(vis[u]^1);
						tot[v]=tot[u]+vis[u];
						q.push(mp(-dis1[v],v));
					}
				}
			}	
		}
		{
			priority_queue<pa>q;
			for (int i=1;i<=n;i++) ds[i]=inf;
			ds[X[1]]=0;
			q.push(mp(-ds[X[1]],X[1]));
			while (!q.empty())
			{
				auto [w,u]=q.top();
				q.pop();
				w=-w;
				if (w!=ds[u]) continue;
				for (auto v:G[u])
				{
					if (ds[v]>ds[u]+(vis[v]))
					{
						ds[v]=ds[u]+(vis[v]);
						q.push(mp(-ds[v],v));
					}
				}
			}	
		}
	}
	for (int i=2;i<=K;i++)
	{
		s[1]+=dis[X[i]];s[2]-=dis[X[i]];
		s[2]+=2;
		if (tot[X[i]])
		{
			int now=dis[X[i]]+(tot[X[i]]-1)*2,now1=dis1[X[i]]+tot[X[i]]-1;
			int del=now1-now;
			if (del+tot[X[i]]+1<=n) 
			{
				s[del+tot[X[i]]+1]-=1;
			}
		}
	}
	
	if (K>500)
	{
		for (int i=1;i<=n;i++)  ans[i]=inf;
		ans[X[1]]=0;
		for (int i=1;i<=n;i++)  s[i]+=s[i-1];
		for (int i=1;i<=n;i++)  s[i]+=s[i-1];
		int lim=n/(K-1);
		for (int i=1;i<=n;i++) 
			for (int j=0;j<=lim;j++)
				f[i][j]=inf;
		f[X[1]][0]=0;
		static pa q[50000005];
		int h=0,t=0;
		q[++t]=mp(X[1],0);
		while (h<t)
		{
			auto [u,d]=q[++h];
			for (auto v:G[u])
			{
				int dd=ds[u]+d+vis[v]-ds[v];
				if (dd<=lim&&f[v][dd]==inf)
				{
					f[v][dd]=f[u][d]+1;
					q[++t]=mp(v,dd);
				}
			}
		}
		for (int i=1;i<=n;i++) 
		{
			if (i==X[1])
			{
				continue;
			}
			for (int j=ds[i];j<=min(ds[i]+lim,n);j++)
			{
				if (f[i][j-ds[i]]==inf) continue;
				ans[i]=min(ans[i],f[i][j-ds[i]]
				+s[j-vis[i]]);
			}
		}
	} else
	{
		// return;
		for (int i=1;i<=n;i++) ans[i]=inf;
		for (int i=1;i<=n;i++) 
		{
			s[i]+=s[i-1];
			if (i>1) ss[i]=ss[i-1]+s[i];
		}
		for (int j=1;j<=n;j++)
			dis1[j]=inf;
		for (int i=1;i<=n;i++)
		{
			priority_queue<pa>q;
			q.push(mp(-0ll,-X[1]));
			while (!q.empty())
			{
				auto [w,u]=q.top();
				q.pop();
				w=-w;
				if (u>0&&dis1[u]!=w) continue;
				if (u<0) u=-u;
				for (auto v:G[u])
					if (dis1[v]>w+1+vis[v]*s[1])
					{
						dis1[v]=w+1+vis[v]*s[1];
						if (!vis[v])
						{
							q.push(mp(-dis1[v],v));
						}
					}
			}
		}
		for (int i=1;i<=n;i++) 
			if (dis1[i]!=inf) ans[i]=dis1[i]-vis[i]*s[1];
		for (int i=1;i<=n;i++) 
			if (!vis[i]) dis1[i]=inf;
		ans[X[1]]=0;
		int tot=0;
		for (int i=2;i<=n;)
		{
			int nxt=i;
			while (nxt<=n&&s[nxt]==s[i]) nxt++;
			priority_queue<pa>q;
			for (int j=1;j<=n;j++)
			{
				if (dis1[j]!=inf)
					q.push(mp(-dis1[j],-j));
				dis[j]=inf;
			}
			bool bl=0;
			while (!q.empty())
			{
				auto [w,u]=q.top();
				q.pop();
				w=-w;
				if (u>0&&dis[u]!=w) continue;
				if (u<0) u=-u;
				for (auto v:G[u])
					if (dis[v]>w+1+vis[v]*s[i])
					{
						dis[v]=w+1+vis[v]*s[i];
						q.push(mp(-dis[v],v));
					}
			}
			for (int j=1;j<=n;j++)
				if (j!=X[1])
				{
					int nw=dis[j];
					if (nw==inf) continue;
					nw+=ss[i-1]-s[i]*(i-2);
					ans[j]=min(ans[j],nw-vis[j]*s[i]);
				}
			tot++;
			i=nxt;
		}
	}
	for (int i=1;i<=n;i++) cout<<ans[i]<<'\n';
		
			
		
}
signed main()
{
	IOS;
	cin.tie(0);
	int T=1;
	while (T--)
	{
		BellaKira();
	}
}
/*#include<bits/stdc++.h>

#define vc vector
#define pb emplace_back
#define pii pair<int, int>
#define mkp make_pair
#define tup tuple <int, int, int>
#define mkt make_tuple
#define rep(i, a, b) for(int i = (a); i <= (b); ++i)
#define lep(i, a, b) for(int i = (a); i >= (b); --i)

#define int long long

using namespace std;
bool ST;

mt19937 gen(time(0));

inline int read() {
	int x = 0, w = 0; char ch = getchar(); while(!isdigit(ch)) w |= (ch == '-'), ch = getchar();
	while(isdigit(ch)) x = x * 10 + (ch ^ 48), ch = getchar(); return w ? -x : x; 
}

const int N = 5e4 + 5, B = 230, inf = 1e16;

int n, m, k, st, key[N], ans[N];
int f[N], g[N], h[N], val[N], ok[N], dp[N][B + 5];
char str[N];
vc <int> G[N], S;
set <pii> slope;

inline void init_g () {
	vc <int> vis (n + 1, 0);
	rep (i, 1, n) g[i] = inf; 
	priority_queue <pii, vc <pii>, greater <pii> > Q; Q.push (mkp (g[st] = 0, st));
	while (!Q.empty ()) {
		auto [d, x] = Q.top (); Q.pop (); 
		if (vis[x]) continue; vis[x] = 1; 
		d += (key[x] && x != st);
		for (auto y : G[x]) if (!vis[y] && d < g[y])
			Q.push (mkp (g[y] = d, y));
	}
}

inline void init_f () {
	vc <int> vis (n + 1, 0);
	priority_queue <pii, vc <pii>, greater <pii> > Q;
	rep (i, 1, n) 
		if (key[i]) Q.push (mkp (f[i] = 0, i));
		else f[i] = inf;
	while (!Q.empty ()) {
		auto [d, x] = Q.top (); Q.pop (); 
		if (vis[x]) continue; vis[x] = 1; 
		for (auto y : G[x]) if (!vis[y] && d + 1 < f[y])
			Q.push (mkp (f[y] = d + 1, y));
	}
	rep (x, 1, n) if (key[x]) {
		f[x] = 2;
		for (auto y : G[x]) if (key[y]) f[x] = ok[x] = 1;
	}
}

inline void init_h () {
	vc <int> vis (n + 1, 0);
	priority_queue <pii, vc <pii>, greater <pii> > Q;
	rep (i, 1, n) 
		if (ok[i]) Q.push(mkp (h[i] = 0, i));
		else h[i] = inf;
	while (!Q.empty ()) {
		auto [d, x] = Q.top (); Q.pop ();
		if (vis[x]) continue; vis[x] = 1;
		d += (!key[x]);
		for (auto y : G[x]) if (!vis[y] && d < h[y])
			Q.push (mkp (h[y] = d, y));
	}
}

namespace case1 {
	inline void solve () {
		int lmt = n / k + 1; 
		rep (i, 0, n) rep (j, 0, lmt) dp[i][j] = inf;
		vc < vc<bool> > vis (n + 1, vc <bool> (lmt + 5, 0));
		priority_queue <tup, vc <tup>, greater <tup> > Q; 
		Q.push (mkt (dp[st][0] = 0, st, 0));
		int cnt = 0;
		while (!Q.empty ()) {
			auto [d, x, v] = Q.top (); Q.pop ();
			if (vis[x][v]) continue; vis[x][v] = 1;
			ans[x] = min (ans[x], d + val[g[x] + v]);
			v += g[x] + (key[x] && x != st);
			for (auto y : G[x]) if (v <= g[y] + lmt && d + 1 < dp[y][v - g[y]])
				Q.push (mkt (dp[y][v - g[y]] = d + 1, y, v - g[y]));
		}
	}
}

namespace case2 {
	inline void dij (int v, int ad, int fl = 0) {
		vc< vc <int> > vis (n + 1, vc <int> (2, 0)), dis (n + 1, vc <int> (2, inf));
		priority_queue <tup, vc <tup>, greater <tup> > Q; 
		Q.push (mkt (dis[st][0] = 0, st, 0));
		while (!Q.empty ()) {
			auto [d, x, u] = Q.top (); Q.pop ();
			if (vis[x][u]) continue; vis[x][u] = 1;
			ans[x] = min (ans[x], d + ad);
			if (u) {
				int z = ((key[x] && x != st) ? v : 0) + 1;
				if (fl && (key[x] && x != st)) continue;
				for (auto y : G[x]) if (d + z < dis[y][1]) 
					Q.push (mkt (dis[y][1] = d + z, y, 1));
			}
			else {
				int w = (key[x] && x != st), z = (fl ? w * val[1] : 0) + 1;
				for (auto y : G[x]) if (d + z < dis[y][w]) 
					Q.push (mkt (dis[y][w] = d + z, y, w));
			}
		}
	}
	inline void solve () {
		dij (inf, 0, 1);
		for (auto [u, v] : slope) 
			dij (v, val[u] - (u - 1) * v);
	}
}

bool ED;
signed main() {
	cerr << (&ED - &ST) / 1024 / 1024 << "MB ---------------------------" << endl;
	
	n = read (); m = read (); k = read ();
	rep (i, 1, n) ans[i] = inf; 
	for (int i = 1, u, v; i <= m; i++) 
		u = read (), v = read (), G[u].pb (v), G[v].pb (u);
	
	scanf ("%s", str + 1);
	rep (i, 1, n) key[i] = str[i] - '0';
	
	rep (i, 1, k) S.pb (read ()); st = S[0];
	
	init_g ();
	init_f ();
	init_h ();
	// solve function 
	{
		// y = x + h[i]
		// y = 2x + f[i] - 2
		auto crs = [&] (int u) -> int {
			return min (n, max (1ll, h[u] - f[u] + 2));
		} ;
		vc <int> ad (n + 1, 0); int K = 0, sum = 0, tmp;
		rep (i, 1, k - 1) {
			sum += f[S[i]];
			ad[1] += 2; ad[tmp = crs (S[i])] --;
		} 
		rep (i, 1, n) {
			val[i] = sum;
			K += ad[i]; sum += K; 
			if (ad[i]) slope.insert (mkp (i, K));
		}
	}
	
	if (k > B) case1 :: solve ();
	else case2 :: solve ();
	
	rep (i, 1, n) printf ("%lld\n", ans[i]);
	
	return 0;
}
#include<bits/stdc++.h>

#define vc vector
#define pb emplace_back
#define pii pair<int, int>
#define mkp make_pair
#define tup tuple <int, int, int>
#define mkt make_tuple
#define rep(i, a, b) for(int i = (a); i <= (b); ++i)
#define lep(i, a, b) for(int i = (a); i >= (b); --i)

#define int long long

using namespace std;
bool ST;

mt19937 gen(time(0));

inline int read() {
	int x = 0, w = 0; char ch = getchar(); while(!isdigit(ch)) w |= (ch == '-'), ch = getchar();
	while(isdigit(ch)) x = x * 10 + (ch ^ 48), ch = getchar(); return w ? -x : x; 
}

const int N = 5e4 + 5, B = 230, inf = 1e16;

int n, m, k, st, key[N], ans[N];
int f[N], g[N], h[N], val[N], ok[N], dp[N][B + 5];
char str[N];
vc <int> G[N], S;
set <pii> slope;

inline void init_g () {
	vc <int> vis (n + 1, 0);
	rep (i, 1, n) g[i] = inf; 
	priority_queue <pii, vc <pii>, greater <pii> > Q; Q.push (mkp (g[st] = 0, st));
	while (!Q.empty ()) {
		auto [d, x] = Q.top (); Q.pop (); 
		if (vis[x]) continue; vis[x] = 1; 
		d += (key[x] && x != st);
		for (auto y : G[x]) if (!vis[y] && d < g[y])
			Q.push (mkp (g[y] = d, y));
	}
}

inline void init_f () {
	vc <int> vis (n + 1, 0);
	priority_queue <pii, vc <pii>, greater <pii> > Q;
	rep (i, 1, n) 
		if (key[i]) Q.push (mkp (f[i] = 0, i));
		else f[i] = inf;
	while (!Q.empty ()) {
		auto [d, x] = Q.top (); Q.pop (); 
		if (vis[x]) continue; vis[x] = 1; 
		for (auto y : G[x]) if (!vis[y] && d + 1 < f[y])
			Q.push (mkp (f[y] = d + 1, y));
	}
	rep (x, 1, n) if (key[x]) {
		f[x] = 2;
		for (auto y : G[x]) if (key[y]) f[x] = ok[x] = 1;
	}
}

inline void init_h () {
	vc <int> vis (n + 1, 0);
	priority_queue <pii, vc <pii>, greater <pii> > Q;
	rep (i, 1, n) 
		if (ok[i]) Q.push(mkp (h[i] = 0, i));
		else h[i] = inf;
	while (!Q.empty ()) {
		auto [d, x] = Q.top (); Q.pop ();
		if (vis[x]) continue; vis[x] = 1;
		d += (!key[x]);
		for (auto y : G[x]) if (!vis[y] && d < h[y])
			Q.push (mkp (h[y] = d, y));
	}
}

namespace case1 {
	inline void solve () {
		int lmt = n / k + 1; 
		rep (i, 0, n) rep (j, 0, lmt) dp[i][j] = inf;
		vc < vc<bool> > vis (n + 1, vc <bool> (lmt + 5, 0));
		priority_queue <tup, vc <tup>, greater <tup> > Q; 
		Q.push (mkt (dp[st][0] = 0, st, 0));
		int cnt = 0;
		while (!Q.empty ()) {
			auto [d, x, v] = Q.top (); Q.pop ();
			if (vis[x][v]) continue; vis[x][v] = 1;
			ans[x] = min (ans[x], d + val[g[x] + v]);
			v += g[x] + (key[x] && x != st);
			for (auto y : G[x]) if (v <= g[y] + lmt && d + 1 < dp[y][v - g[y]])
				Q.push (mkt (dp[y][v - g[y]] = d + 1, y, v - g[y]));
		}
	}
}

namespace case2 {
	inline void dij (int v, int ad, int fl = 0) {
		vc< vc <int> > vis (n + 1, vc <int> (2, 0)), dis (n + 1, vc <int> (2, inf));
		priority_queue <tup, vc <tup>, greater <tup> > Q; 
		Q.push (mkt (dis[st][0] = 0, st, 0));
		while (!Q.empty ()) {
			auto [d, x, u] = Q.top (); Q.pop ();
			if (vis[x][u]) continue; vis[x][u] = 1;
			ans[x] = min (ans[x], d + ad);
			if (u) {
				int z = ((key[x] && x != st) ? v : 0) + 1;
				if (fl && (key[x] && x != st)) continue;
				for (auto y : G[x]) if (d + z < dis[y][1]) 
					Q.push (mkt (dis[y][1] = d + z, y, 1));
			}
			else {
				int w = (key[x] && x != st), z = (fl ? w * val[1] : 0) + 1;
				for (auto y : G[x]) if (d + z < dis[y][w]) 
					Q.push (mkt (dis[y][w] = d + z, y, w));
			}
		}
	}
	inline void solve () {
		dij (inf, 0, 1);
		for (auto [u, v] : slope) 
			dij (v, val[u] - (u - 1) * v);
	}
}

bool ED;
signed main() {
	cerr << (&ED - &ST) / 1024 / 1024 << "MB ---------------------------" << endl;
	
	n = read (); m = read (); k = read ();
	rep (i, 1, n) ans[i] = inf; 
	for (int i = 1, u, v; i <= m; i++) 
		u = read (), v = read (), G[u].pb (v), G[v].pb (u);
	
	scanf ("%s", str + 1);
	rep (i, 1, n) key[i] = str[i] - '0';
	
	rep (i, 1, k) S.pb (read ()); st = S[0];
	
	init_g ();
	init_f ();
	init_h ();
	// solve function 
	{
		// y = x + h[i]
		// y = 2x + f[i] - 2
		auto crs = [&] (int u) -> int {
			return min (n, max (1ll, h[u] - f[u] + 2));
		} ;
		vc <int> ad (n + 1, 0); int K = 0, sum = 0, tmp;
		rep (i, 1, k - 1) {
			sum += f[S[i]];
			ad[1] += 2; ad[tmp = crs (S[i])] --;
		} 
		rep (i, 1, n) {
			val[i] = sum;
			K += ad[i]; sum += K; 
			if (ad[i]) slope.insert (mkp (i, K));
		}
	}
	
	if (k > B) case1 :: solve ();
	else case2 :: solve ();
	
	rep (i, 1, n) printf ("%lld\n", ans[i]);
	
	return 0;
}
*/