#include<bits/stdc++.h>
#define int long long
#define rg register
#define il inline
#define TT(T, Args) template<typename T, typename... Args>
#define L(i, a, b) for (rg int i = (a); i <= (b); i++)
#define R(i, a, b) for (rg int i = (a); i >= (b); i--)
#define rep(i, a) for (rg auto i : a)
using namespace std;
namespace xmpl_{
	il int rd(){
		int f = 1, x = 0;
		char ch = getchar();
		while(ch < '0' || ch > '9'){
			if (ch == '-') f = -1;
			ch = getchar();
		}
		while(ch >= '0' && ch <= '9'){
			x = x * 10 + ch - '0';
			ch = getchar();
		}
		return x * f;
	}
	TT(T, Args) il void rd(T &x){
		int f = 1;
		x = 0;
		char ch = getchar();
		while(ch < '0' || ch > '9'){
			if (ch == '-') f = -1;
			ch = getchar();
		}
		while(ch >= '0' && ch <= '9'){
			x = x * 10 + ch - '0';
			ch = getchar();
		}
		x *= f;
	}
	TT(T, Args) il void rd(T &x, Args &...args){rd(x), rd(args...);}
	TT(T, Args) il void rdArr(T *arr, int cnt){while(cnt--) rd(*arr), arr++;}
	il void wt(int x){
		if (x < 0){
			putchar('-');
			x = -x;
		}
		if (x > 9) wt(x / 10);
		putchar(x % 10 + 48);
	}
	il void wtln(int x){wt(x), putchar('\n');}
	il void wtsp(int x){wt(x), putchar(' ');}
	il void swap(int &x, int &y){x ^= y ^= x ^= y;}
	il int max(int x, int y){return (x > y ? x : y);}
	il int min(int x, int y){return (x < y ? x : y);}
	il void ckmax(int &x, int y){x = max(x, y);}
	il void ckmin(int &x, int y){x = min(x, y);}
	il void cksum(int &x, int y){x += y;}
	TT(T, Args) il void ckmax(T &x, T y, Args &...args){ckmax(x, y), ckmax(x, args...);}
	TT(T, Args) il void ckmin(T &x, T y, Args &...args){ckmin(x, y), ckmin(x, args...);}
	TT(T, Args) il void cksum(T &x, T y, Args &...args){cksum(x, y), cksum(x, args...);}
}
using namespace xmpl_;
using namespace std;

const int N = 1e6 + 5, M = 21, K = 1e6 + 5, inf = 0x3f3f3f3f3f3f3f3f;
int n, m, k, u, v, a[N], b[N], d[N], f[N];
vector<int> g[N], ng[N], fg[N], p[N];
queue<int> q;
int dfn[N], low[N], times, cur, bel[N];
vector<int> scc[N];
stack<int> st;
bool in_st[N], vis[N];

il void init(){

}

il void clear(){
	
}

il void Tarjan(int u){
	dfn[u] = low[u] = ++times, st.push(u), in_st[u] = 1;
	rep(v, g[u]){
		if (!dfn[v]){
			Tarjan(v);
			ckmin(low[u], low[v]);
		}
		else if (in_st[v]) ckmin(low[u], dfn[v]);
	}
	if (dfn[u] == low[u]){
		cur++;
		int x = st.top();
		bel[x] = cur, scc[cur].push_back(x), in_st[x] = 0, st.pop();
		while(x ^ u){
			x = st.top();
			bel[x] = cur, scc[cur].push_back(x), in_st[x] = 0, st.pop();
		}
	}
}

il void work(){
	rd(n, m, k), rdArr(a + 1, n), rdArr(b + 1, k);
	L(i, 1, k) p[b[i]].push_back(i);
	L(i, 1, m){
		rd(u, v);
		g[u].push_back(v);
	}
	L(i, 1, n) if (!dfn[i]) Tarjan(i);
	L(u, 1, n){
		rep(v, g[u]){
			if (bel[u] ^ bel[v]) ng[bel[u]].push_back(bel[v]), fg[bel[v]].push_back(bel[u]), d[bel[u]]++;
		}
	}
	memset(f, 0x3f, sizeof(f));
	L(i, 1, cur){
		if (!d[i]) q.push(i);
	}
	while(q.size()){
		int u = q.front();
		q.pop();
		if (scc[u].size() > 1){
			// sort(scc[u].begin(), scc[u].end(), cmp);
			// rep(v, scc[u]){
			// 	if (a[v] <= k && a[v] < f[u] - 1) f[u] = a[v];
			// }

			// vector<int> vec;
			// rep(v, scc[u]) rep(it, p[a[v]]) vec.push_back(it);
			// sort(vec.begin(), vec.end(), greater<int>());
			// rep(v, vec) if (v < f[u] - 1) f[u] = v;
			int ans = inf / 2, sgn = 0;
			rep(v, scc[u]){
				vis[a[v]] = 1;
				if (!p[a[v]].empty()) ckmin(ans, p[a[v]][0]);
			}
			L(i, ans, f[u] - 1){
				if (!vis[b[i]]) break;
				sgn++;
			}
			if (sgn & 1) ckmin(f[u], ans);
			else ckmin(f[u], ans + 1);
		}
		rep(v, fg[u]){
			ckmin(f[v], f[u]);
			// if (scc[u].size() == 1 && a[scc[u][0]] <= k && a[scc[u][0]] < f[u] - 1) ckmin(f[v], a[scc[u][0]]);
			if (scc[u].size() == 1 && !p[a[scc[u][0]]].empty()){
				int c = p[a[scc[u][0]]][0];
				if (c <= k && c < f[u] - 1) ckmin(f[v], c);
			}
			if (!(--d[v])) q.push(v);
		}
	}
	L(i, 1, n) cout << ((f[bel[i]] > k * 2 ? -1 : f[bel[i]] - 1)) << " ";
}

signed main(){
	// #define file 114514
#ifdef file	
	freopen("code.in", "r", stdin);
	freopen("code.out", "w", stdout);
#endif
	// init();
	int t = 1;
	// t = rd();
	while(t--){
		// clear();
		work();
		// puts("");
	}
	return 0;
}