#include "beechtree.h"
#include <bits/stdc++.h>
using namespace std;
#define sp " "
#define endl "\n"
#define fileio() freopen("input.txt", "r", stdin), freopen("output.txt", "w", stdout)
#define fastio() cin.tie(0), ios_base::sync_with_stdio(0)
#define pb push_back
#define pii pair<int, int>
#define st first
#define nd second
#define LL node * 2
#define RR node * 2 + 1
#define ll long long
#define MAXN 300005
vector<pii> adj[MAXN];
int sz[MAXN];
void dfs(int node){
sz[node] = 1;
for (auto i :adj[node]){
dfs(i.st);
sz[node] += sz[i.st];
}
}
vector<int> beechtree(int N, int M, std::vector<int> P, std::vector<int> C)
{
for (int i = 0; i < N; i++) adj[i].clear();
for (int i = 1; i < N; i++){
adj[P[i]].pb({i, C[i]});
}
dfs(0);
for (int i = 0; i < N; i++){
sort(adj[i].begin(), adj[i].end(), [&](pii a, pii b){
return adj[a.st].size()> adj[b.st].size();
});
}
int n = N;
vector<int> ans(N, 1);
for (int i = n - 1; i >= 0; i--){
vector<int> curr, cnt(M + 2, 0);
queue<int> q;
q.push(i);
curr.pb(i);
while(!q.empty()){
int top = q.front();
q.pop();
for (auto j : adj[top]){
if (curr[cnt[C[j.st]]] != P[j.st]) ans[i] = 0;
curr.pb(j.st);
cnt[C[j.st]]++;
q.push(j.st);
}
}
}
return ans;
}
/*
int main()
{
fileio();
int N, M;
assert(2 == scanf("%d %d", &N, &M));
std::vector<int> P(N);
for (int i = 0; i < N; ++i)
assert(1 == scanf("%d", &P[i]));
std::vector<int> C(N);
for (int i = 0; i < N; ++i)
assert(1 == scanf("%d", &C[i]));
fclose(stdin);
std::vector<int> res = beechtree(N, M, P, C);
int n = res.size();
for (int i = 0; i < n; ++i)
{
if (i > 0)
printf(" ");
printf("%d", res[i]);
}
printf("\n");
fclose(stdout);
return 0;
}*/
