#pragma GCC optimize("Ofast")
#pragma GCC optimize("O3,unroll-loops")
#include <bits/stdc++.h>
using namespace std;
#define f0r(i, n) for (auto i = 0; i < (n); ++i)
#define fnr(i, n, k) for (auto i = (n); i < (k); ++i)
#define all(v) (v).begin(), (v).end()
#define pb push_back
#define F first
#define S second
#define ctn(x) cout << x << '\n'
#define forl(a, l) for (auto a : l)
#define ctl(l) for (auto &a : (l)) cout << a << ' '; cout << endl;
#define lb(v, x) (lower_bound(all(v), x) - begin(v))
#define ub(v, x) (upper_bound(all(v), x) - begin(v))
#define pq priority_queue
template <class T>
using V = vector<T>;
using ll = long long;
using vi = V<int>;
using vl = V<ll>;
using pi = pair<int, int>;
using ti = tuple<int, int, int>;
using Adj = V<vi>;
using vvi = V<vi>;
#include "beechtree.h"
Adj G;
vi subsz, col;
V<vi> mat;
vi ans;
V<vi> vs;
int m;
void dfs(int v) {
subsz[v] = 1;
set<int> seen;
forl(c, G[v]) {
dfs(c);
if (mat[v][col[c]]) {
ans[v] = 0;
}
else mat[v][col[c]] = subsz[c];
subsz[v] += subsz[c];
ans[v] &= ans[c];
if (!ans[v]) continue;
forl(y, vs[v]) {
fnr(k, 1, m+1) {
ans[v] &= (subsz[c] < subsz[y] && mat[c][k] <= mat[y][k]) || (subsz[c] > subsz[y] && mat[c][k] >= mat[y][k]) || (subsz[c] == subsz[y] && mat[c][k] == mat[y][k]);
}
}
forl(x, vs[c]) vs[v].pb(x);
}
forl(c, G[v]) fnr(k, 1, m+1) {
ans[v] &= mat[c][k] <= mat[v][k];
}
vs[v].pb(v);
}
std::vector<int> beechtree(int N, int M, std::vector<int> P, std::vector<int> C) {
G.assign(N, {});
subsz.assign(N, 0);
col = C;
mat.assign(N, vi(M+1));
fnr(i, 1, N) G[P[i]].pb(i);
vs.assign(N, {});
m = M;
ans.assign(N, 1);
dfs(0);
return ans;
}
