#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;
}
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);
vector<vector<int>> vec;
for (int v : adj[0]) {
vec.pb({});
for (int u : adj[v]) vec.back().pb(u), ans[u] = 1;
sort(ALL(vec.back()), [&](int x, int y) {
return c[x]<c[y];
});
ans[v] = 1;
for (int i=0; i+1 < vec.back().size(); i++) if (c[vec.back()[i]] == c[vec.back()[i+1]]) ans[v] = 0;
}
sort(ALL(vec), [&](auto x, auto y) {
return x.size() < y.size();
});
vec.pb({});
for (int v : adj[0]) vec.back().pb(v);
sort(ALL(vec.back()), [&](int x, int y) {
return c[x]<c[y];
});
ans[0] = 1;
for (int i=0; i+1 < vec.back().size(); i++) if (c[vec.back()[i]] == c[vec.back()[i+1]]) ans[0] = 0;
for (int v : adj[0]) if (ans[v]==0) ans[0] = 0;
for (int i=1; i<vec.size(); i++) if (!is_subset(vec[i-1], vec[i])) ans[0] = 0;
return ans;
}
