#include <bits/stdc++.h>

using namespace std;

const int N = 1e6 + 5, M = 5e6 + 5;

int n, m, k;
int a[N], b[N], pos[N];
int la[N], h[N], ne[M], en[M], idx;
int dfn[N], low[N], dfst;
int sta[N], insta[N], tt;
int scc, bel[N], siz[N], mp[N];
vector<int> col[N];
int g[N], vis[N];

inline void Add(int la[], int a, int b)
{
    ne[ ++ idx] = la[a];
    la[a] = idx;
    en[idx] = b;
}
inline void Tarjan(int u)
{
    dfn[u] = low[u] = ++ dfst;
    insta[sta[ ++ tt] = u] = 1;
    for(int i = la[u]; i; i = ne[i])
    {
        int v = en[i];
        if(!dfn[v])
        {
            Tarjan(v);
            low[u] = min(low[u], low[v]);
        }
        else if(insta[v])
        {
            low[u] = min(low[u], dfn[v]);
        }
    }
    if(low[u] == dfn[u])
    {
        scc ++ ;
        mp[scc] = k + 1;
        int v;
        do{
            insta[v = sta[tt -- ]] = 0;
            bel[v] = scc;
            siz[scc] ++ ;
            if(!vis[a[v]])
            {
                col[scc].push_back(a[v]);
                vis[a[v]] = 1;
                mp[scc] = min(mp[scc], pos[a[v]]);
            }
        }while(v != u);
        for(int i : col[scc]) vis[i] = 0;
    }
}
inline void DP()
{
    for(int u = 1; u <= n; u ++ )
        for(int i = la[u]; i; i = ne[i])
        {
            int v = en[i];
            if(bel[u] != bel[v]) Add(h, bel[u], bel[v]);
        }
    for(int u = 1; u <= scc; u ++ )
    {
        g[u] = k + 1;
        for(int i = h[u]; i; i = ne[i])
        {
            int v = en[i];
            g[u] = min(g[u], g[v]);
            if(mp[v] + 1 < g[v]) g[u] = min(g[u], mp[v]);
        }
        if(siz[u] > 1 && mp[u] < g[u])
        {
            for(int i : col[u]) vis[i] = 1;
            int x = mp[u], y = x;
            while(y < g[u] - 2 && vis[b[y + 1]]) y ++ ;
            g[u] = min(g[u], x + ((y - x) & 1));
            for(int i : col[u]) vis[i] = 0;
        }
    }
}

int main()
{
    scanf("%d%d%d", &n, &m, &k);
    for(int i = 1; i <= n; i ++ ) scanf("%d", &a[i]);
    for(int i = 1; i <= k; i ++ ) scanf("%d", &b[i]), !pos[b[i]] && (pos[b[i]] = i);
    for(int i = 1; i <= m; i ++ )
    {
        int a, b;
        scanf("%d%d", &a, &b);
        Add(la, a, b);
    }
    for(int i = 1; i <= n; i ++ )
        if(!dfn[i])
            Tarjan(i);
    DP();
    for(int i = 1; i <= n; i ++ ) printf("%d ", g[bel[i]] <= k ? g[bel[i]] - 1 : -1);
    puts("");
    return 0;
}