#include "beechtree.h"
#include <bits/stdc++.h>
using namespace std;
#define pb push_back
#define ALL(a) a.begin(), a.end()
const int MXN = 200200;
int n;
int m;
vector<int> p;
vector<int> c;
vector<int> adj[MXN];
bool is_subset(vector<int> a, vector<int> b) {
set<int> all;
for (int x : b) all.insert(c[x]);
for (int x : a) if (!all.contains(c[x])) return false;
return true;
}
bool is_unq(vector<int> a) {
sort(ALL(a), [&](int x, int y) {
return c[x]<c[y];
});
for (int i=0; i+1 < a.size(); i++) if (c[a[i]] == c[a[i+1]]) return false;
return true;
}
vector<int> beechtree(int N, int M, vector<int> P, vector<int> C) {
n = N;
m = M;
p = P;
c = C;
for (int i=1; i<n; i++) adj[p[i]].pb(i);
vector<int> ans(n);
auto dfs = [&](auto self, int v) -> vector<int> {
vector<vector<int>> vec;
for (int u : adj[v]) {
vec.pb({});
auto res = self(self, u);
for (int it : res) if (it != u) vec.back().pb(it);
}
sort(ALL(vec), [&](auto x, auto y) {
return x.size() < y.size();
});
vec.pb(adj[v]);
ans[v] = 1;
for (int u : adj[v]) if (ans[u]==0) ans[v]=0;
if (!is_unq(vec.back())) ans[v]=0;
for (int i=0; i+1 < vec.size(); i++) if (!is_subset(vec[i], vec[i+1])) ans[v]=0;
vector<int> ret;
for (auto x : vec) for (auto y : x) ret.pb(y);
return ret;
};
dfs(dfs, 0);
return ans;
}
