#include<bits/stdc++.h>
#define L(i, j, k) for(int i = (j); i <= (k); i++)
#define R(i, j, k) for(int i = (j); i >= (k); i--)
#define ll long long
#define ull unsigned long long 
#define sz(a) ((int) a.size())
#define vi vector<int>
#define me(a, x) memset(a, x, sizeof(a))
using namespace std;
const int N = 4e5 + 7;
int n, m;
int fa[N], col[N];
vi e[N];

int ans[N], siz[N];
int ord[N], top;

int cnt[N];
inline int check(int rt) {
	priority_queue < pair < ll, int > > q;
	q.push({siz[rt], rt}); 
	
	top = 0;
	while(!q.empty()) {
		int x = q.top().second;
//		cout << "x = " << x << ' ' << rt << endl;
		q.pop();
		
		ord[++top] = x;
		if(x != rt) {
			int r = ++cnt[col[x]];
			if(fa[x] != ord[r]) {
				L(j, 1, top) cnt[col[ord[j]]] = 0;
//				cout << "lost " << rt << ' ' << r << endl;
				return false;
			} 
		}
		
		for(auto v : e[x]) {
			q.push({(ll)siz[v] * n + - top, v});
		} 
	} 
	
	L(j, 1, top) cnt[col[ord[j]]] = 0;
	return true;
}

vi beechtree(int N, int M, vi P, vi C) {
	n = N, m = M; 
	L(i, 2, n) {
		fa[i] = P[i - 1] + 1;
		col[i] = C[i - 1];
		e[fa[i]].emplace_back(i);
	}
	
	L(i, 1, n) siz[i] = 1;
	R(i, n, 2) {
		siz[fa[i]] += siz[i]; 
	}
	L(i, 1, n) {
		if(check(i)) {
			ans[i] = 1;
		}
	}
	
	vi ret(n);
	L(i, 0, n - 1) {
		ret[i] = ans[i + 1];
	}
	return ret;
}
//int main () { 
//	ios :: sync_with_stdio(false);
//	cin.tie (0); cout.tie (0);
////	vi ans = beechtree(4, 2, vi{-1, 0, 0, 0}, vi{0, 1, 1, 2});
////	vi ans = beechtree(18, 3, 
//// vi{-1, 0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 10, 11, 11},
//// vi{0, 1, 2, 3, 1, 2, 3, 1, 3, 3, 2, 1, 1, 2, 2, 1, 2, 3});
//	vi ans = beechtree(7, 2, vi{-1, 0, 1, 1, 0, 4, 5}, vi{0, 1, 1, 2, 2, 1, 1}); 
//	L(i, 0, sz(ans) - 1) cout << ans[i] << ' ';
//	cout << endl;
//	return 0;
//}