#include "beechtree.h"
#include <bits/stdc++.h>
//#define int long long
#define pii pair<int,int>
#define vi vector<int>
#define ff first
#define ss second
#define sp << " " <<
#define all(x) x.begin(),x.end()
using namespace std;
const int LIM = 2e5+1;
vector<pii> edges[LIM];
vi ans(LIM,0),C,P;
int N;
vi ctr(LIM,0);
bool check(int node) {
for (auto it : edges[node]) {
ctr[it.ss] = 0;
}
for (auto it : edges[node]) {
if (ctr[it.ss]) return false;
ctr[it.ss]++;
}
if (node) return true;
for (auto it : edges[node]) if (!check(it.ff)) return false;
sort(all(edges[node]),[&](pii a,pii b) {
return edges[a.ff].size() > edges[b.ff].size();
});
ctr.assign(N,0);
for (int i = 0;i<N;i++) ctr[C[i]]++;
for (int i = 0;i<edges[node].size();i++) {
for (auto it : edges[edges[node][i].ff]) {
if (ctr[C[it.ff]] < i+1) return false;
}
}
return true;
}
int dfs(int node) {
for (auto it : edges[node]) dfs(it.ff);
return ans[node] = check(node);
}
std::vector<int> beechtree(int N_, int M, std::vector<int> P_, std::vector<int> C_)
{
N = N_;
P = P_,C = C_;
ans.assign(N_,0);
for (int i = 0;i<N;i++) edges[i].clear();
vi v;
for (auto it : C) v.push_back(it);
sort(all(v));
v.erase(unique(all(v)),v.end());
for (auto& it : C) it = lower_bound(all(v),it)-v.begin();
for (int i = 1;i<N;i++) {
edges[P[i]].push_back({i,C[i]});
}
dfs(0);
return ans;
}
