#include "beechtree.h"
#include "bits/stdc++.h"
#define pb push_back
#define popb pop_back
#define fi first
#define sc second
#define si(a_) (ll)(a_.size())
#define all(a_) a_.begin(),a_.end()
using namespace std;
using ll = int;
using pll = pair<ll,ll>;
const ll maxn = 200005;
ll n,m;
vector<pll> g[maxn];
bool ok[maxn];
vector<int> ans;
ll up[maxn];
ll c[maxn];
ll cnt[maxn];
bool oksub(ll i){
bool oke = 1;
for(pll p : g[i]){
ll j = p.fi,col = p.sc;
if(cnt[col]) oke = 0;
cnt[col] = 1;
}
for(pll p : g[i]){
ll j = p.fi,col = p.sc;
cnt[col] = 0;
}
return oke;
}
std::vector<int> beechtree(int N, int M, std::vector<int> P, std::vector<int> C)
{
n = N,m = M;
for(ll i = 2;i<=n;i++){
ll par = P[i-1]+1;
g[par].pb({i,C[i-1]});
up[i] = par;
c[i] = C[i-1];
}
ans.resize(n);
for(ll i = 0;i<n;i++) ans[i] = 0;
for(ll i = 2;i<=n;i++){
if(up[i]!=1&&up[up[i]]==1){
ans[i-1] = 1;
}else if(up[i]==1){
ans[i-1] = oksub(i);
}
}
if(oksub(1)){
set<ll> s1,s2;
ans[0] = 1;
map<ll,ll> mp;
for(pll p : g[1]){
ll u = p.fi,col = p.sc;
if(ans[u-1]==0) ans[0] = 0;
s1.insert(col);
for(pll q : g[u]){
s2.insert(q.sc);
mp[q.sc]++;
}
}
for(ll x : s2) if(s1.find(x)==s1.end()) ans[0] = 0;
vector<ll> v;
for(pll p : g[1]){
ll u = p.fi;
ll mx = 0;
for(pll q : g[u]){
mx = max(mx,mp[q.sc]);
}
v.pb(mx);
}
sort(all(v));
for(ll i = 0;i<si(v);i++){
if(i+1<v[i]) ans[0] = 0;
}
}
return ans;
}
