#include<iostream>
#include<cstdio>
#include<vector>
#include<set>
#define N 1000000
using namespace std;
const int inf=(int)(1e9);
int read()
{
	char c=0;
	int sum=0;
	while (c<'0'||c>'9') c=getchar();
	while ('0'<=c&&c<='9') sum=sum*10+c-'0',c=getchar();
	return sum;
}
struct reads
{
	int num,type;
	bool operator < (const reads &t)const
	{
		return num!=t.num?num<t.num:type<t.type;
	}
};
reads w[N+1];
struct rds
{
	int num,data;
	bool operator < (const rds &t)const
	{
		return num<t.num;
	}
};
set<rds>s;
int n,m,k,leng,ps[N+1],belong[N+1],minn[N+1],in[N+1],cater,L[N+1],R[N+1],a[N+1],b[N+1],dfn[N+1],low[N+1],delta[N+1],stk[N+1],top,ans[N+1],dque[N+1],l=1,r;
bool used[N+1],vis[N+1];
vector<int>E[N+1];
vector<int>v[N+1];
vector<int>ES[N+1];
vector<int>st[N+1];
void tarjan(int x)
{
	dfn[x]=low[x]=++leng,used[x]=1,stk[++top]=x;
	for (int i=0;i<E[x].size();++i)
	{
		if (!dfn[E[x][i]]) tarjan(E[x][i]),low[x]=min(low[x],low[E[x][i]]);
		else if (used[E[x][i]]) low[x]=min(low[x],dfn[E[x][i]]);
	}
	if (dfn[x]==low[x])
	{
		++cater;
		while (stk[top]!=x) belong[stk[top]]=cater,v[cater].push_back(stk[top]),used[stk[top]]=0,top--;
		belong[stk[top]]=cater,v[cater].push_back(stk[top]),belong[stk[top]]=cater,used[stk[top]]=0,top--;
	}
	return;
}
int main()
{
	int top,x,y,res;
	n=read(),m=read(),k=read();
	for (int i=1;i<=n;++i) a[i]=read(),minn[i]=inf,w[i]=(reads){inf,0};
	for (int i=1;i<=k;++i) b[i]=read(),minn[b[i]]=min(minn[b[i]],i);
	for (int i=1;i<=n;++i) delta[i]=minn[a[i]];
	for (int i=1;i<=m;++i) x=read(),y=read(),E[x].push_back(y);
	for (int i=1;i<=n;++i)
		if (!dfn[i])
			tarjan(i);
	for (int i=1;i<=n;++i)
		for (int j=0;j<E[i].size();++j)
			if (belong[i]!=belong[E[i][j]])
				ES[belong[E[i][j]]].push_back(belong[i]),in[belong[i]]++;
	for (int i=1;i<=cater;++i)
		if (!in[i])
			dque[++r]=i;
	for (int i=1;i<=cater;++i)
	{
		res=inf;
		for (int j=0;j<v[i].size();++j) res=min(res,delta[v[i][j]]);
		L[i]=res;
		if (v[i].size()!=1&&res!=inf) st[res].push_back(i);
		else R[i]=res;
	}
	for (int i=k;i>=1;--i)
	{
		if (!ps[b[i]]) s.insert((rds){i,b[i]});
		else s.erase((rds){ps[b[i]],b[i]}),ps[b[i]]=i,s.insert((rds){i,b[i]});
		for (int j=0;j<st[i].size();++j)
		{
			for (int k=0;k<v[st[i][j]].size();++k) vis[a[v[st[i][j]][k]]]=1;
			res=k;
			for (auto it:s)
				if (!vis[it.data])
				{
					res=it.num-1;
					break;
				}
			R[st[i][j]]=res;
			for (int k=0;k<v[st[i][j]].size();++k) vis[a[v[st[i][j]][k]]]=0;
		}
	}
	while (l<=r)
	{
		top=dque[l++];
		if (w[top].num<=L[top])
		{
			for (int i=0;i<v[top].size();++i) ans[v[top][i]]=w[top].num+w[top].type-1;
		}
		else if (w[top].num==inf)
		{
			if (v[top].size()==1) ans[v[top][0]]=-1;
			else
			{
				for (int i=0;i<v[top].size();++i) ans[v[top][i]]=L[top]+((R[top]-L[top])&1)-1;
			}
		}
		else
		{
			if (v[top].size()==1) ans[v[top][0]]=w[top].num+w[top].type-1;
			else
			{
				if (w[top].num>R[top]+1)
				{
					for (int i=0;i<v[top].size();++i) ans[v[top][i]]=L[top]+((R[top]-L[top])&1)-1;
				}
				else
				{
					for (int i=0;i<v[top].size();++i) ans[v[top][i]]=L[top]+(((w[top].num-L[top])&1)^w[top].type)-1;
				}
			}
		}
		if (w[top].num>L[top])
		{
			if (w[top].num>R[top]+1) w[top]=(reads){L[top],(R[top]-L[top])&1};
			else w[top]=(reads){L[top],((w[top].num-L[top])&1)^w[top].type};
		}
		for (int i=0;i<ES[top].size();++i)
		{
			w[ES[top][i]]=min(w[ES[top][i]],w[top]),in[ES[top][i]]--;
			if (!in[ES[top][i]]) dque[++r]=ES[top][i];
		}
	}
	for (int i=1;i<=n;++i) printf("%d ",ans[i]);
	puts("");
	return 0;
}