//A tree without skin will surely die.
//A man without face will be alive.
#include<bits/stdc++.h>
using namespace std;
#define all(x) (x).begin(),(x).end()
#define rep(i,j,k) for(int i=j;i<=k;++i)
#define per(i,j,k) for(int i=j;i>=k;--i)
int const N=1e6+10;
int n,m,k,a[N],b[N],f[N],co[N],rd[N],dfn[N],low[N],cnt,s[N],top;
vector<int>e[N],E[N],V[N],vec[N];bool vis[N];
inline void tarjan(int x){
	dfn[x]=low[x]=++cnt,vis[x]=1,s[++top]=x;
	for (auto v:e[x])
		if (!dfn[v]) tarjan(v),low[x]=min(low[x],low[v]);
		else if (vis[v]) low[x]=min(low[x],dfn[v]);
	if (dfn[x]==low[x]){
		++co[0];
		while (1){
			int X=s[top--];
			co[X]=co[0],vis[X]=0,V[co[0]].push_back(X);
			if (X==x) break;
		}
	}
}
inline void solve(){
	cin>>n>>m>>k;
	rep(i,1,n) cin>>a[i];
	rep(i,1,k) cin>>b[i],vec[b[i]].push_back(i);
	memset(f,0x3f,sizeof(f));
	rep(i,1,m){
		int u,v;cin>>u>>v;
		e[u].push_back(v);
	}
	rep(i,1,n) if (!dfn[i]) tarjan(i);
	rep(i,1,n) for (auto j:e[i])
		if (co[i]^co[j]) E[co[j]].push_back(co[i]),++rd[co[i]];
	queue<int>q;
	rep(i,1,co[0]) if (!rd[i]) q.push(i);
	while (!q.empty()){
		int x=q.front();q.pop();
		if (V[x].size()>1){
			int it=1e9;
			for (auto y:V[x]){
				vis[a[y]]=1;
				if (vec[a[y]].size()) it=min(it,vec[a[y]][0]);
			}
			if (it+1<f[x]){
				int sm=0;
				rep(i,it,f[x]-1)
					if (!vis[b[i]]) break;
					else ++sm;
				if (sm&1) f[x]=min(f[x],it);
				else f[x]=min(f[x],it+1);
			}
		}
		for (auto v:E[x]){
			f[v]=min(f[v],f[x]);
			if (V[x].size()==1 && !vec[a[V[x][0]]].empty()){
				int val=vec[a[V[x][0]]][0];
				if (val<=k && val+1<f[x]) f[v]=min(f[v],val);
			}
			if (!--rd[v]) q.push(v);
		}
	}
	rep(i,1,n)
		if (f[co[i]]>k) cout<<"-1 ";
		else cout<<f[co[i]]-1<<' ';
	cout<<'\n';
}
signed main(){
	ios::sync_with_stdio(false);
	cin.tie(0),cout.tie(0);
	int t=1;
	// cin>>t;
	while (t--) solve();
	return 0;
}