#include<bits/stdc++.h>
using namespace std;
const int N=1000001;
int n,m,k;
int a[N],b[N],c[N];
vector<int> g[N];
int dfn[N],low[N],now;
int st[N],tp;
bool vis[N];
int cnt,scc[N];
vector<int> adj[N],h[N];
void dfs(int u){
	dfn[u]=low[u]=++now;
	st[++tp]=u;
	vis[u]=1;
	for(int v:g[u]){
		if(!dfn[v]){
			dfs(v);
			low[u]=min(low[u],low[v]);
		}
		else if(vis[v])low[u]=min(low[u],dfn[v]);
	}
	if(dfn[u]==low[u]){
		cnt++;
		while(1){
			int x=st[tp--];
			vis[x]=0;
			scc[x]=cnt;
			adj[cnt].push_back(x);
			for(int v:g[x])if(scc[v])h[cnt].push_back(scc[v]);
			if(x==u)break;
		}
	}
}
int p[N],q[N],d[N];
bool cmp(int i,int j){
	return p[i]<p[j];
}
int mn[N*4],bk[N];
#define mid (l+r>>1)
#define ls (p<<1)
#define rs (p<<1|1)
void build(int p,int l,int r){
	mn[p]=k+1;
	if(l==r)return;
    build(ls,l,mid);
    build(rs,mid+1,r);
}
void modify(int p,int l,int r,int x,int v){
	if(l==r){
		mn[p]=v;
		return;
	}
	if(x<=mid)modify(ls,l,mid,x,v);
	else modify(rs,mid+1,r,x,v);
	mn[p]=min(mn[ls],mn[rs]);
}
int f[N],ans[N];
int main(){
	ios::sync_with_stdio(0);
	cin.tie(0),cout.tie(0);
	cin>>n>>m>>k;
	for(int i=1;i<=n;i++)cin>>a[i],c[i]=k+1;
	for(int i=1;i<=k;i++)cin>>b[i],c[b[i]]=min(c[b[i]],i);
	for(int i=1;i<=m;i++){
		int u,v;
		cin>>u>>v;
		g[u].push_back(v);
	}
	for(int i=1;i<=n;i++)if(!dfn[i])dfs(i);
	for(int i=1;i<=cnt;i++){
		d[i]=i;
		p[i]=k+1;
		for(int x:adj[i])p[i]=min(p[i],c[a[x]]);
	}
	sort(d+1,d+cnt+1,cmp);
	build(1,1,n);
	for(int i=1;i<=n;i++)bk[i]=k+1;
	for(int i=k,j=cnt;i>=1;i--){
		bk[b[i]]=i;
		modify(1,1,n,i,b[i]);
		while(j&&i==p[d[j]]){
			int u=d[j];
			for(int x:adj[u])modify(1,1,n,a[x],k+1);
			q[u]=mn[1];
			for(int x:adj[u])modify(1,1,n,a[x],bk[a[x]]);
			j--;
		}
	}
	for(int i=1;i<=cnt;i++){
		f[i]=k+1;
		ans[i]=-1;
		for(int j:h[i])f[i]=min(f[i],f[j]);
		if(f[i]<k)ans[i]=f[i];
		if(p[i]<f[i]){
			int qq=min(q[i],f[i]);
			if((p[i]+qq)&1)f[i]=p[i]-1;
			else f[i]=p[i];
		}
		if(adj[i].size()>1&&f[i]<k)ans[i]=f[i];
	}
	for(int i=1;i<=n;i++)cout<<ans[scc[i]]<<' ';
	return 0;
}