#include "beechtree.h"
#include<bits/stdc++.h>

using namespace std;

typedef int ll;

vector<ll> beechtree(ll n, ll m, vector<ll> p, vector<ll> c) {
	vector<vector<ll>> sons(n);
	for (ll i = 1; i < n; i++) {
		sons[p[i]].push_back(i);
	}
	map<vector<ll>, vector<ll>> all;
	vector<ll> ans(n, 0);
	vector<ll> cd(n);
	vector<ll> h(n);
	ll nh = 0;
	for (ll j = 0; j < n; j++) {
		cd[j] = sons[j].size();
		if (cd[j] == 0) {
			all[vector<ll>(0)].push_back(j);
		}
	}
	while (!all.empty()) {
		auto[_, now] = *all.begin();
		all.erase(all.begin());
		for (auto j : now) {
			h[j] = nh;
			if (p[j] == -1) {
				continue;
			}
			cd[p[j]]--;
			if (cd[p[j]] == 0) {
				vector<ll> ns;
				for (auto k : sons[p[j]]) {
					ns.push_back(h[k]);
				}
				sort(ns.rbegin(), ns.rend());
				all[ns].push_back(p[j]);
			}
		}
		nh++;
	}
	for (ll i = 0; i < n; i++) {
		set<tuple<ll, ll, ll>> s;
		s.insert(make_tuple(-h[i], -1, i));
		bool b = true;
		map<ll, ll> ncol;
		ll nnum = 0;
		while (!s.empty()) {
			auto[_, need, i] = *s.begin();
			s.erase(s.begin());
			if (need != -1) {
				if (ncol[c[i]] != need) {
					b = false;
					break;
				}
				ncol[c[i]]++;
			}
			for (auto j : sons[i]) {
				s.emplace(-h[j], nnum, j);
			}
			nnum++;
		}
		if (b) {
			ans[i] = 1;
		}
	}
	return ans;
}

#ifdef LOCAL
int main()
{
    int N, M;
    assert(2 == scanf("%d %d", &N, &M));
    std::vector<int> P(N);
    for (int i = 0; i < N; ++i)
        assert(1 == scanf("%d", &P[i]));
    std::vector<int> C(N);
    for (int i = 0; i < N; ++i)
        assert(1 == scanf("%d", &C[i]));

    fclose(stdin);

    std::vector<int> res = beechtree(N, M, P, C);

    int n = res.size();
    for (int i = 0; i < n; ++i)
    {
        if (i > 0)
            printf(" ");
        printf("%d", res[i]);
    }
    printf("\n");
    fclose(stdout);

    return 0;
}
#endif