#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<vector<int>> have(N, vector<int>(2, 0));
    for (int i = N-1; i >= 0; i--) {
        ret[i] = true;
        for (int v : child[i]) {
            maxdeg[i] = max(maxdeg[i], maxdeg[v]);
            have[i][0] += have[v][0];
            have[i][1] += have[v][1];
        }
        if (maxdeg[i] >= 2 || child[i].size() > 2) ret[i] = false;
        maxdeg[i] = max(maxdeg[i], (int)child[i].size());
        for (int v : child[i]) {
            if (have[v][0] > 0 && have[v][1] > 0) ret[i] = false;
        }
        if (i != 0) have[i][C[i]-1]++;
    }
    return ret;
}
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