#include "beechtree.h"

#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }


int N, M;
vector<int> P, C;

vector<int> deg;
vector<vector<int>> graph;
vector<int> colorful;
void dfs(int u) {
  vector<int> cs;
  for (const int v : graph[u]) {
    dfs(v);
    if (!colorful[v]) {
      colorful[u] = 0;
    }
    cs.push_back(C[v]);
  }
  sort(cs.begin(), cs.end());
  for (int j = 0; j < (int)cs.size() - 1; ++j) if (cs[j] == cs[j + 1]) {
    colorful[u] = 0;
  }
}

vector<int> us;
void dfsSub(int u) {
  us.push_back(u);
  for (const int v : graph[u]) {
    dfsSub(v);
  }
}

vector<int> ids;
int check(int r) {
  if (!colorful[r]) {
    return 0;
  }
  us.clear();
  dfsSub(r);
  const int usLen = us.size();
  sort(us.begin(), us.end(), [&](int u, int v) -> bool {
    return ((deg[u] != deg[v]) ? (deg[u] > deg[v]) : (u < v));
  });
  if (r != us[0]) {
    return 0;
  }
  for (int j = 0; j < usLen; ++j) {
    ids[us[j]] = usLen;
  }
  ids[r] = 0;
  for (int j = 1, k = 1; j < usLen; j = k) {
    for (; k < usLen && deg[us[j]] == deg[us[k]]; ++k) {}
    sort(us.begin() + j, us.begin() + k, [&](int u, int v) -> bool {
      return ((ids[P[u]] != ids[P[v]]) ? (ids[P[u]] < ids[P[v]]) : (u < v));
    });
    for (int l = j; l < k; ++l) {
      ids[us[l]] = l;
    }
  }
  vector<int> cnt(M, 0);
  for (int j = 1; j < usLen; ++j) {
    const int u = us[j];
    if (P[u] != us[cnt[C[u]]]) {
      return 0;
    }
    ++cnt[C[u]];
  }
  return 1;
}

vector<int> run() {
  deg.assign(N, 0);
  graph.assign(N, {});
  for (int u = 1; u < N; ++u) {
    ++deg[P[u]];
    graph[P[u]].push_back(u);
  }
  colorful.assign(N, 1);
  dfs(0);
  
  vector<int> ans(N, 0);
  ids.resize(N);
  for (int r = 0; r < N; ++r) {
    ans[r] = check(r);
  }
  return ans;
}

std::vector<int> beechtree(int N_, int M_, std::vector<int> P_, std::vector<int> C_)
{
  N = N_;
  M = M_;
  P = P_;
  C = C_;
  for (int u = 0; u < N; ++u) {
    --C[u];
  }
  return run();
}