#ifndef CYBER
#include "beechtree.h"
#endif
#ifdef CYBER
#include "grader.cpp"
#endif
#include <bits/stdc++.h>
#define lg long long

using namespace std;

const lg N = 2e5+5;

vector<int> adj[N], ans;
lg st[N], en[N], tim;

void dfs(lg src)
{
	st[src] = ++tim;
	for(auto it : adj[src])
	{
		dfs(it);
	}
	en[src] = tim;
}

std::vector<int> beechtree(int N, int M, std::vector<int> P, std::vector<int> C)
{
	ans.resize(N);
	for(int i = 0; i <= N; i++)	st[i] = en[i] = tim = 0, adj[i].clear();
	for(int i = 1; i < N; i++)
	{
		adj[P[i]].push_back(i);
	}
	if(N <= 8)
	{
		dfs(0);
		for(int i = 0; i < N; i++)
		{
			vector<lg> x;
			for(int j = 0; j < N; j++)
			{
				if(st[i] <= st[j] && en[j] <= en[i])
				{
					x.push_back(j);
				}
			}
			if(x.size() == 1)
			{
				ans[i] = 1;
				continue;
			} 
			ans[i] = 0;
			do{
				map<int, int> mp;
				lg b = 1;
				for(int j = 1; j < x.size(); j++)
				{
					if(P[x[j]] != x[mp[C[x[j]]]])
					{
						b = 0;
					}
					mp[C[x[j]]]++;
				}
				if(b)
				{
					ans[i] = 1;
					break;
				}
			}
			while(next_permutation(x.begin()+1, x.end()));
		}
		return ans;
	}
	lg linear = 1;
	for(int i = 1; i < N; i++)
	{
		linear &= (P[i] == i-1);
	}
	if(linear)
	{
		set<int> se;
		for(int i = N-1; i >= 0; i--)
		{
			ans[i] = (se.size() <= 1 ? 1 : 0);
			se.insert(C[i]);
		}
	}
	else{
		for(int i = 1; i < N; i++)	ans[i] = 1;
		set<lg> se2;
		lg z = 0;
		for(auto it : adj[0])
		{
			set<int> se;
			for(auto it2 : adj[it])
			{
				se.insert(C[it2]);
				se2.insert(C[it2]);
			}
			se2.insert(C[it]);
			if(se.size() > 1)
			{
				ans[it] = 0;
			}
		}
		ans[0] = (se2.size() <= 1);
	}
    return ans;
}