#include"beechtree.h"
#include<algorithm>
#include<set>
#include<iostream>
#include<map>
#include<queue>
using namespace std;
int n;
vector<int>ch[200000];
map<int,int>ch_col[200000];
int par[200000];
int col[200000];
bool bad[200000];
int sub[200000];
bool res[200000];
void dfs1(int node){
sub[node]=1;
for(int c:ch[node]){
dfs1(c);
sub[node]+=sub[c];
}
}
void dfs2(int node){
bad[node]=ch[node].size()!=ch_col[node].size();
for(int c:ch[node]){
dfs2(c);
bad[node]|=bad[c];
}
}
bool good(int a,int b){
for(auto[c,i]:ch_col[b])
if(ch_col[a][c]<i)
return false;
return true;
}
// merge into s1
bool merge(set<pair<int,int>>&s1,set<pair<int,int>>&s2){
bool res=true;
for(auto i:s2){
auto iter=s1.insert(i).first;
auto iter2=iter,iter3=iter;
if(iter3!=s1.begin()){
iter3--;
if(!good(iter->second,iter3->second))
res=false;
}
iter2++;
if(iter2!=s1.end()&&!good(iter2->second,iter->second))
res=false;
}
return res;
}
set<pair<int,int>>get(int node){
res[node]=!bad[node];
set<pair<int,int>>s;
s.insert({sub[node],node});
for(int c:ch[node]){
auto r=get(c);
res[node]&=res[c];
if(r.size()>s.size())
swap(s,r);
if(!merge(s,r))
res[node]=false;
}
return s;
}
vector<int>beechtree(int N,int M,vector<int>P,vector<int>C){
n=N;
for(int i=0;i<n;i++)
ch[i].clear();
for(int i=0;i<n;i++){
par[i]=P[i];
if(i)
ch[par[i]].push_back(i);
col[i]=C[i];
}
dfs1(0);
for(int i=0;i<n;i++){
ch_col[i].clear();
for(int c:ch[i])
ch_col[i][col[c]]=sub[c];
}
dfs2(0);
get(0);
vector<int>res2(n);
for(int i=0;i<n;i++)
res2[i]=res[i];
return res2;
}
