#include "beechtree.h"
#include "bits/stdc++.h"
using namespace std;
#define rep(i,a,b) for(int i = a;i < b;i++)
#define trav(nx, v) for(auto &nx: v)
#define sz(v) (int) v.size()
#define all(v) begin(v), end(v)
#define pb push_back
#define fi first
#define se second
int dx[] = {1, 0, -1, 0};
int dy[] = {0, 1, 0, -1};
const int LIM = 200000;
typedef int LL;
vector <int> edge[LIM + 5];
LL warna[LIM + 5];
vector <int> ans;

LL dfs(LL pos){
	LL can = -1;
	trav(nx, edge[pos]){
		auto nxColor = dfs(nx);
		if(nxColor == warna[nx]) can = warna[nx];
	}
	ans[pos] = sz(edge[pos]) == 0 || can;
	if(sz(edge[pos]) == 0) return warna[pos];
	return can;
}

std::vector<int> beechtree(int N, int M, std::vector<int> P, std::vector<int> C){
	rep(i,1,N){
		edge[P[i]].pb(i);
	}
	rep(i,0,N){
		warna[i] = C[i];
	}
	ans.resize(N);
	dfs(0);
	return ans;
}