#include <bits/stdc++.h>
using namespace std;
const int N = 1e5 + 100;
int n, k, par[N], a[N], h[N], ans[N], sub_ans[N];
map<int, int> cnt[N], anc, sac[N];
vector<int> g[N];
deque<int> dq[N];
bool good[N];
void dfs(int v){
cnt[a[v]][h[v]]++;
if (anc.find(a[v]) == anc.end()) good[v] = 1;
anc[a[v]]++;
for (int u : g[v]){
h[u] = h[v] + 1;
dfs(u);
}
anc[a[v]]--;
if (anc[a[v]] == 0) anc.erase(a[v]);
}
void calc(int v){
int mx = -1;
for (int u : g[v]){
calc(u);
if (mx == -1 or dq[u].size() > dq[mx].size())
mx = u;
}
if (mx == -1){
dq[v].push_front(1);
sac[v][a[v]]++;
if (good[v]) ans[v] = 1, sub_ans[v] = 1;
return ;
}
swap(dq[v], dq[mx]);
swap(sac[v], sac[mx]);
for (int u : g[v]){
if (u == mx) continue;
for (int i = 0; i < dq[u].size(); i ++)
dq[v][i] += dq[u][i];
for (auto [val, c] : sac[u])
sac[v][val] += c;
}
dq[v].push_front(1);
sac[v][a[v]]++;
if (!good[v]) return ;
for (auto [lvl, c] : cnt[a[v]]){
int l = lvl - h[v];
if (l < 0) continue;
ans[v] += min(c, dq[v][l]);
}
sub_ans[v] = sac[v][a[v]];
}
int main(){
cin >> n >> k;
for (int i = 0; i < n; i ++)
cin >> a[i];
for (int i = 1; i < n; i ++)
cin >> par[i], g[par[i]].push_back(i);
dfs(0);
calc(0);
int mx = 0, mn = n;
for (int v = 0; v < n; v ++){
if (!good[v]) continue;
if (mx < ans[v] or (mx == ans[v] and mn > (ans[v] - sub_ans[v])))
mx = ans[v], mn = ans[v] - sub_ans[v];
}
cout << mx << " " << mn << endl;
}
