#include <bits/stdc++.h>
using namespace std;
#define pb push_back
#define sz(a) (int)a.size()
#define all(a) begin(a),end(a)
using ar2 = array<int,2>;
const int mxN = (int)1e5+10;
const int INF = (int)1e9;
int n, k;
vector<int> adj[mxN];
ar2 ans{0,-INF};
vector<int> col[mxN];
int a[mxN], dep[mxN], sub[mxN];
vector<int> S[mxN];
set<ar2> Dep[mxN];
int dfs_timer, st[mxN], en[mxN];
void dfs1(int s, int p){
sub[s] = 1; st[s]=++dfs_timer;
if(p!=-1) dep[s]=dep[p]+1;
for(auto u : adj[s]){
if(u==p) continue;
dfs1(u,s); sub[s]+=sub[u];
}
en[s] = dfs_timer;
}
bool upper(int a, int b){
return st[a]<=st[b] and en[a]>=en[b];
}
void dfs(int s, int p){
S[s].pb(s); Dep[s].insert({dep[s],1});
for(auto u : adj[s]){
if(u==p) continue;
dfs(u,s);
if(sz(S[s]) < sz(S[u])) S[s].swap(S[u]), Dep[s].swap(Dep[u]);
for(auto v : S[u]) S[s].pb(v);
for(auto [v,w] : Dep[u]){
auto itr = Dep[s].lower_bound({v,-1});
if(itr!=end(Dep[s]) and (*itr)[0]==v){
int cur = (*itr)[1];
Dep[s].erase(itr);
Dep[s].insert({v,cur+w});
}
else Dep[s].insert({v,w});
}
}
if(min(sub[s],sz(col[a[s]])) < ans[0]) return;
auto cur = ar2({0,0});
unordered_map<int,int> tot; tot.clear();
for(auto u : col[a[s]]){
if(upper(s,u)) cur[0]++,tot[dep[u]]++;
}
for(auto u : col[a[s]]){
if(upper(s,u)) continue;
auto itr = Dep[s].lower_bound({dep[u],-1});
if(itr!=end(Dep[s]) and (*itr)[0]==dep[u]){
if(tot[dep[u]] < (*itr)[1]){
cur[0]++, cur[1]--; tot[dep[u]]++;
}
}
}
ans = max(ans, cur);
}
int main(){
cin >> n >> k;
for(int i = 0; i < n; i++){
cin >> a[i]; col[a[i]].pb(i);
}
for(int i = 1; i < n; i++){
int x; cin >> x; adj[i].pb(x), adj[x].pb(i);
}
dfs1(0,-1);
for(int i = 0; i < n; i++)
sort(all(adj[i]),[&](int a, int b){return sub[a]>sub[b]; });
dfs(0,-1); cout << ans[0] << " " << -ans[1] << "\n";
}
