#include "beechtree.h"
#include<bits/stdc++.h>
#define int long long
#define f0r(i,n) for(int i = 0; i<n; i++)
#define pb push_back
#define mp make_pair
#define vi vector<int>
#define mii map<int,int>
#define pii pair<int,int>
#define vpii vector<pii>
#define FOR(i, k, n) for(int i = k; i<n; i++)
#define vb vector<bool>
#define vout(v) for(auto u : v)cout<<u<<' '; cout<<endl;
using namespace std;
vector<vi>adj, colset, su, cha;
vi dep, sts, die, diesum, tp;
vector<signed>ans; int M;
int dfs(int node){
	int cur = 1;
	for(auto u : adj[node]){
		dep[u] = dep[node] + 1;
		cur += dfs(u);
	}
	sts[node] = cur;
	return cur;
}
int d2(int node){
	int cur = die[node];
	for(auto u : adj[node]){
		cur += d2(u);
	}
	diesum[node] = cur;
	return cur;
}
void d3(int node){
	if(sts[node] == 1){
		su[node][tp[node]]++; return;
	}
	for(auto u : adj[node]){
		d3(u);
		f0r(j, 4){
			su[node][j] += su[u][j];
		}
	}
	su[node][tp[node]]++;
}
void d4(int node){
	if(sts[node] == 1){
		cha[node] = {0};
		return;
	}
	
	vector<pair<vi, int>>w;
	for(auto u : adj[node]){
		d4(u);
		w.pb(mp(cha[u], u));
	}
	
	sort(w.rbegin(), w.rend());
	adj[node].clear();
	for(auto u : w){
		adj[node].pb(u.second);
	}
	queue<int>q;
	vi seq;
	q.push(node); seq.pb(adj[node].size());
	while(!q.empty()){
		int node = q.front(); q.pop();
		for(auto u : adj[node]){
			q.push(u); seq.pb(adj[u].size());
		}
	}
	cha[node] = seq;
	
}
void solve(int node){
	if(sts[node] == 1){
		ans[node] = 1; return;
	}
	for(auto u : adj[node]){
		solve(u);
	}
	if(diesum[node] != 0){
		ans[node] = 0; return;
	}
	
	//test if including the next for loop preserves correct ans
	
	for(auto u : adj[node]){
		if(ans[u] == 0){
			ans[node] = 0; return;
		}
	}
	/*
	vi w = su[node];
	//vout(w);
	if(tp[node] == 1 && w[3] != 0){
		ans[node] = 0; return;
	}
	if(tp[node] == 2 && w[3] != 0){
		ans[node] = 0; return;
	}
	if(w[1] != 0 && w[2] != 0){
		ans[node] = 0; return;
	}
	ans[node] = 1; return;
	*/
	queue<int>q;
	vi seq;
	q.push(node); seq.pb(node);
	while(!q.empty()){
		int node = q.front(); q.pop();
		for(auto u : adj[node]){
			q.push(u); seq.pb(u);
		}
	}
	set<int>vis;
	f0r(i, M){
		vis.insert(i + 1);
	}
	bool ok = 1;
	f0r(i, seq.size()){
		set<int>ne;
		for(auto u : colset[seq[i]]){
			if(!vis.count(u))ok = 0;
			ne.insert(u);
		}
		/*
		for(auto u : vis)cout<<u<<' ';
		cout<<'\n';
		for(auto u : ne)cout<<u<<' ';
		cout<<'\n';
		*/
		if(!ok)break;
		vis = ne;
	}
	ans[node] = ok;
	
}
std::vector<signed> beechtree(signed N, signed M, std::vector<signed> P, std::vector<signed> C)
{
	::M = M;
	ans.resize(N);
	FOR(i, 1, N)ans[i] = 0;
	colset.clear(); colset.resize(N); adj.clear(); adj.resize(N); tp.clear(); tp.resize(N);
	dep.clear(); dep.resize(N); sts.clear(); sts.resize(N); die.clear(); die.resize(N); diesum.clear(); diesum.resize(N);
	cha.resize(N);
	FOR(i, 1, N){
		adj[P[i]].pb(i);
	}
	
	f0r(i, N){
		set<int>tmp;
		for(auto u : adj[i]){
			tmp.insert(C[u]); colset[i].pb(C[u]);
		}
		if(tmp.size() != colset[i].size()){
			die[i] = 1;
		}
		int sum = 0;
		for(auto u : tmp){
			sum += u;
		}
		tp[i] = sum;
	}
	dfs(0);
	d2(0);
	//for adj of each node, sort them by size of colset
	/*
	f0r(i,N){
		vpii w;
		for(auto u : adj[i]){
			w.pb(mp(colset[u].size(), u));
			sort(w.rbegin(), w.rend());
		}
		adj[i].clear();
		for(auto u : w){
			adj[i].pb(u.second);
		}
	}
	*/
	d4(0);
	/*
	su.resize(N);
	f0r(i, N){
		su[i].resize(4);
	}
	d3(0);
	solve(0);
	*/
	solve(0);
	return ans;
}
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