#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
const int N = 1e5 + 10;
vector<int> nei[N], cols[N], Ver[N], lev[N], vc;
vector<pair<int,int>> Vec;
int st[N], en[N], alr[N], Seen[N], cnt[N], cur, a[N];
void dfs(int u, int p, int h){
st[u] = cur++;
cols[h].push_back(a[u]);
Ver[h].push_back(st[u]);
Vec.push_back({h, a[u]});
alr[u] = cnt[a[u]]++;
Seen[a[u]]++;
if (Seen[a[u]] == 1)
vc.push_back(u);
for (int i : nei[u]){
if (i == p) continue;
dfs(i, u, h + 1);
}
Seen[a[u]]--;
alr[u] = cnt[a[u]] - alr[u];
en[u] = cur++;
}
int check(int rt, int ans = 0){
for (int i : lev[a[rt]]){
int m1 = upper_bound(begin(cols[i]), end(cols[i]), a[rt]) - upper_bound(begin(cols[i]), end(cols[i]), a[rt] - 1);
int m2 = upper_bound(begin(Ver[i]), end(Ver[i]), en[rt]) - upper_bound(begin(Ver[i]), end(Ver[i]), st[rt] - 1);
ans += min(m1, m2);
}
return ans;
}
int main(){
int n, k, p, Ans1 = 0, Ans2;
cin>>n>>k;
for (int i=1;i<=n;i++)
cin>>a[i];
for (int i=2;i<=n;i++){
cin>>p;
nei[p + 1].push_back(i);
}
dfs(1, 1, 1);
sort(begin(Vec), end(Vec));
for (int i=1;i<=n;i++){
sort(begin(Ver[i]), end(Ver[i]));
sort(begin(cols[i]), end(cols[i]));
}
for (auto [i, j] : Vec){
if (lev[j].size() == 0 or lev[j].back() != i)
lev[j].push_back(i);
}
for (int i : vc){
int ret = check(i);
if (ret > Ans1)
Ans1 = ret, Ans2 = ret - alr[i];
else if (ret == Ans1)
Ans2 = min(Ans2, ret - alr[i]);
}
cout<<Ans1<<" "<<Ans2<<'\n';
}
