#include "beechtree.h"
#include <bits/stdc++.h>
using namespace std;
typedef vector <int> vec;
#define pb push_back
typedef pair <int, int> pii;
const int N = 2e5 + 5;
int siz[N], c[N], key[N], h[N], seq[N], ans[N]; vec fa, w, son[N], p;
void dfs(int u) {
	p. pb(u);
	for (int v : son[u]) dfs(v);
}
bool chk(int i) {
	if (!~ h[i]) return 1;
	p. clear(), dfs(i), sort (p. begin(), p. end(), [] (const int &u, const int &v) { return siz[u] > siz[v]; });
	for (int j=0; j<siz[i]; ) {
		int k = j;
		while (k < siz[i] && siz[p[k]] == siz[p[j]])
			key[p[k]] = ! k ? 0 : key[fa[p[k]]], k ++;
		sort (p. begin() + j, p. begin() + k, [] (const int &u, const int &v) { return key[u] < key[v]; });
		for (; j<k; j++) key[p[j]] = j;
	} bool f = 1;
	for (int j : p) {
		if (j == i) continue;
		if (p[c[w[j]]] ^ fa[j]) { f = 0; break; }
		c[w[j]] ++;
	}
	for (int j : p) c[w[j]] = 0;
	return f;
}
void solve(int u) {
	if (!~ h[u]) return void (ans[u] = 1);
	int len = 0;
	for (int v=u; ~v; v=h[v]) seq[++len] = v;
	int l = 1, r = len, t;
	while (l < r) {
		int mid = l + r >> 1;
		if (chk(seq[mid])) r = mid;
		else l = mid + 1;
	} ans[t=seq[r]] = 1;
	for (; u^t; u=h[u])
		for (int v : son[u])
			if (v ^ h[u])
				solve(v);
}
vec beechtree(int n, int m, vec fa, vec w) {
	:: fa = fa, :: w = w;
	for (int i=1; i<n; i++)
		son[fa[i]]. pb(i);
	for (int i=n-1; ~i; i--) {
		siz[i] = 1;
		for (int j : son[i]) siz[i] += siz[j];
		if (! son[i]. empty()) {
			h[i] = son[i][0];
			for (int j : son[i])
				if (siz[j] > siz[h[i]])
					h[i] = j;
		} else h[i] = - 1;
	} solve(0);
	for (int i=1; i<n; i++) ans[i] |= ans[fa[i]];
	return vec (ans, ans+n);
}