#include "beechtree.h"
#include <bits/stdc++.h>
using namespace std;
vector<int> beechtree(int N, int M, vector<int> P, vector<int> C) {
    vector<int> ret(N);
    vector<vector<int>> child(N);
    for (int i = 1; i < N; i++) child[P[i]].push_back(i);
    
    vector<int> maxdeg(N);
    vector<int> have1(N), have2(N);
    for (int i = N-1; i >= 0; i--) {
        for (int v : child[i]) {
            maxdeg[i] = max(maxdeg[i], maxdeg[v]);
            have1[i] += have1[v]-(C[v] == 1);
            have2[i] += have2[v]-(C[v] == 2);
        }
        if (maxdeg[i] >= 2 || (have1[i] > 0 && have2[i] > 0)) ret[i] = false;
        else ret[i] = true;
        maxdeg[i] = max(maxdeg[i], (int)child[i].size());
        if (C[i] == 1) have1[i]++;
        else have2[i]++;
        for (int v : child[i]) {
            have1[i] += (C[v] == 1);
            have2[i] += (C[v] == 2);
        }
    }
    return ret;
}
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