#include <cstdio>
#include <vector>
#include <algorithm>
#include <queue>
using namespace std;
int n,m,K,u,v,a[1000005],b[1000005],ord[1000005],cnt,belong[1000005],occ[1000005],mnocc[1000005],mn[4000005],mn2[1000005],old[1000005],mnto[1000005],deg[1000005],f[1000005];
bool vis[1000005];
vector <int> g[1000005],rg[1000005],scc[1000005],q[1000005],h[1000005],fr[1000005];
queue <int> qq;
void update(int pos){
    mn[pos] = min(mn[pos << 1],mn[pos << 1 | 1]);
}
void build(int pos,int l,int r){
    if(l == r){
        mn[pos] = mn2[l] = K + 1;
        return;
    }
    int mid = (l + r) >> 1;
    build(pos << 1,l,mid);
    build(pos << 1 | 1,mid + 1,r);
    update(pos);
}
void modify(int pos,int l,int r,int p,int x){
    if(l == r){
        mn[pos] = mn2[l] = x;
        return;
    }
    int mid = (l + r) >> 1;
    if(p <= mid){
        modify(pos << 1,l,mid,p,x);
    }
    else{
        modify(pos << 1 | 1,mid + 1,r,p,x);
    }
    update(pos);
}
void dfs1(int pos){
    vis[pos] = 1;
    for(int i = 0;i < g[pos].size();i++){
        if(!vis[g[pos][i]]){
            dfs1(g[pos][i]);
        }
    }
    ord[++cnt] = pos;
}
void dfs2(int pos){
    scc[belong[pos] = cnt].push_back(pos);
    mnocc[cnt] = min(mnocc[cnt],occ[a[pos]]);
    for(int i = 0;i < rg[pos].size();i++){
        if(!belong[rg[pos][i]]){
            dfs2(rg[pos][i]);
        }
    }
}
int main(){
    scanf("%d%d%d",&n,&m,&K);
    for(int i = 1;i <= n;i++){
        scanf("%d",&a[i]);
        occ[i] = K + 1;
    }
    for(int i = 1;i <= K;i++){
        scanf("%d",&b[i]);
        if(occ[b[i]] == K + 1){
            occ[b[i]] = i;
        }
    }
    for(int i = 1;i <= m;i++){
        scanf("%d%d",&u,&v);
        g[u].push_back(v);
        rg[v].push_back(u);
    }
    for(int i = 1;i <= n;i++){
        if(!vis[i]){
            dfs1(i);
        }
    }
    cnt = 0;
    for(int i = n;i;i--){
        if(!belong[ord[i]]){
            cnt++;
            mnocc[cnt] = mnto[cnt] = f[cnt] = K + 1;
            dfs2(ord[i]);
            q[mnocc[cnt]].push_back(cnt);
        }
    }
    build(1,1,n);
    for(int i = K;i;i--){
        modify(1,1,n,b[i],i);
        for(int j = 0;j < q[i].size();j++){
            for(int k = 0;k < scc[q[i][j]].size();k++){
                old[k] = mn2[a[scc[q[i][j]][k]]];
                modify(1,1,n,a[scc[q[i][j]][k]],K + 1);
            }
            mnto[-q[i][j]] = mn[1];
            for(int k = 0;k < scc[q[i][j]].size();k++){
                modify(1,1,n,a[scc[q[i][j]][k]],old[k]);
            }
        }
    }
    for(int i = 1;i <= n;i++){
        for(int j = 0;j < rg[i].size();j++){
            if(belong[i] != belong[rg[i][j]]){
                h[belong[i]].push_back(belong[rg[i][j]]);
                fr[belong[i]].push_back(i);
                deg[belong[rg[i][j]]]++;
            }
        }
    }
    for(int i = 1;i <= cnt;i++){
        if(!deg[i]){
            qq.push(i);
        }
    }
    while(qq.size()){
        int tmp = qq.front();
        qq.pop();
        if(scc[tmp].size() > 1){
            mnocc[tmp] = min(mnocc[tmp],f[tmp]);
            mnto[tmp] = min(mnto[tmp],f[tmp]);
            f[tmp] = mnocc[tmp] - ((mnto[tmp] - mnocc[tmp]) & 1);
        }
        for(int i = 0;i < h[tmp].size();i++){
            f[h[tmp][i]] = min(f[h[tmp][i]],f[tmp]);
            if(occ[a[fr[tmp][i]]] < f[tmp]){
                f[h[tmp][i]] = min(f[h[tmp][i]],occ[a[fr[tmp][i]]] - 1);
            }
            if(!(--deg[h[tmp][i]])){
                qq.push(h[tmp][i]);
            }
        }
    }
    for(int i = 1;i <= n;i++){
        if(f[belong[i]] <= K){
            printf("%d ",f[belong[i]]);
        }
        else{
            printf("-1 ");
        }
    }
    return 0;
}