#include <bits/stdc++.h>
using namespace std;
#pragma GCC optimize ("Ofast")
#pragma GCC target ("avx2")
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<long long, long long> pll;
#define el << '\n'
#define nl cout << '\n'
#define spc << ' '
#define forn(i,n) for (int i=0; i<n; i++)
#define forl(i,s,e) for (int i=s; i<e; i++)
#define pb push_back
#define fi first
#define se second
#define rsz resize
#define sz(x) ((int) x.size())
#define all(x) x.begin(), x.end()
const int inf = 1000000000;
const ll inf2 = 4000000000000000000;

const int MAXN = 200005;

map<int, int> ch[MAXN];
vector<int> ach[MAXN];
bool mc[MAXN];
int ss[MAXN];

set<pii> st[MAXN];

bool eq(int a, int b) {
	for (pii i : ch[a]) {
		if (ch[b].find(i.fi) == ch[b].end()) return false;
		if (ss[ch[b][i.fi]] != ss[i.se]) return false;
	}
	return true;
}

bool sts(int a, int b) {
	for (pii i : ch[a]) {
		if (ch[b].find(i.fi) == ch[b].end()) return false;
		if (ss[ch[b][i.fi]] < ss[i.se]) return false;
	}
	return true;
}

void dfs(int cn) {
	ss[cn] = 1;
	for (int i : ach[cn]) {
		dfs(i);
		ss[cn] += ss[i];
	}
	for (int i : ach[cn]) mc[cn] &= mc[i];
	if (!mc[cn]) return;
	assert (sz(ch[cn]) == sz(ach[cn]));
	for (int i : ach[cn]) {
		if (sz(st[i]) > sz(st[cn])) swap(st[i], st[cn]);
		for (pii j : st[i]) {
			auto ptr = st[cn].lower_bound({j.fi, -1});
			if (ptr == st[cn].end()) {
				if (!sts((*st[cn].rbegin()).se, j.se)) {
					mc[cn] = false;
					return;
				}
				st[cn].insert(j);
			}
			auto temp = *ptr;
			if (temp.fi == j.fi) {
				if (!eq(temp.se, j.se)) {
					mc[cn] = false;
					return;
				}
			}
			else {
				if (!sts(j.se, temp.se)) {
					mc[cn] = false;
					return;
				}
				st[cn].insert(j);
			}
		}
	}
	if (sz(st[cn])) {
		auto temp = *(st[cn].rbegin());
		if (!sts(temp.se, cn)) {
			mc[cn] = false;
			return;
		}
	}
	st[cn].insert({ss[cn], cn});
}

vector<int> beechtree(int N, int M, vector<int> P, vector<int> C) {
	forn(i,N) mc[i] = true;
	forl(i,1,N) {
		if (ch[P[i]].find(C[i]) == ch[P[i]].end()) ch[P[i]][C[i]] = i;
		else mc[P[i]] = false;
		ach[P[i]].pb(i);
	}
	dfs(0);
	vector<int> ans(N);
	forn(i,N) ans[i] = mc[i];
	return ans;
}