#include <bits/stdc++.h>
#define int long long

using namespace std;
const int N = 5e5 + 5;
int c[N];
vector<int> gr[N];
int dp[N];
set<int> q[N];
int idx[N];
void dfs(int x , int p) {
    for (int i : gr[x]) {
        if (i != p) {
            dfs(i , x);
        }
    }
    if (c[x] != 0) {
        q[x].insert(c[x]);
        idx[x] = x;
        dp[x] = 1;
    } else {
        for (int i : gr[x]) {
            if (i == p) continue;
            if (q[idx[x]].size() < q[idx[i]].size()) idx[x] = idx[i];
        }
        for (int i : gr[x]) {
            if (idx[x] == idx[i] || i == p) continue;
            for (int j : q[idx[i]]) {
                q[idx[x]].insert(j);
            }
        }
        dp[x] = q[idx[x]].size();
    }

}

int32_t main()
{
    ios_base::sync_with_stdio(0);
    int n , k;
    cin>>n>>k;
    for (int i = 0; i < n ; ++ i) {
        cin>>c[i];
    }
    for (int i = 1 ; i < n ; ++ i) {
        int vv ;
        cin>>vv;
        --vv;
        gr[vv].push_back(i);
        gr[i].push_back(vv);
    }
    dfs(0, -1);
    for (int i = 0; i < n ; ++ i) {
        cout<<dp[i]<<' ';
    }
}