#include <bits/stdc++.h>
using namespace std;
int n, k;
int p[100000], depths[100000], colours[100000];
int jmp[100000][22];
vector<int> child[100000];
vector<int> groups[100000];
map<int,int> depthcnt[100000];
int best, ans;
void dfs(int i, int depth) {
depths[i] = depth;
for (int u: child[i]) dfs(u,depth+1);
}
int lca(int a, int b) {
if (depths[b] < depths[a]) swap(a,b);
for (int i = 20; i >= 0; i--) if (depths[jmp[b][i]] >= depths[a]) b = jmp[b][i];
if (b!=a) {
for (int i = 20; i >= 0; i--) if (jmp[a][i] != jmp[b][i]) {
a = jmp[a][i];
b = jmp[b][i];
}
}
if (a!=b) return jmp[a][1];
else return a;
}
void find(int i) {
depthcnt[i][depths[i]]++;
for (int u: child[i]) {
find(u);
if (depthcnt[u].size() > depthcnt[i].size()) swap(depthcnt[u],depthcnt[i]);
for (pair<int,int> j: depthcnt[u]) depthcnt[i][j.first] += j.second;
}
map<int,int> m, m2;
for (int j: groups[colours[i]]) {
m[depths[j]]++;
m2[depths[j]] = depthcnt[i][depths[j]];
}
int res = 1;
for (int j: groups[colours[i]]) {
if (j!=i && lca(j,i) == i) {
res++;
m[depths[j]]--;
m2[depths[j]]--;
}
}
int swapped = 0;
for (pair<int,int> j: m) if (j.first > depths[i]) swapped += min(j.second, m2[j.first]);
if (swapped+res > best) {
best = swapped+res;
ans = swapped;
}
else if (swapped+res == best) {
if (swapped < ans) ans = swapped;
}
// cout << res << " " << swapped << "\n";
// cout << "\n\n";
// // cout << i << " " << depths[i] << ":\n";
// // for (pair<int,int> u: depthcnt[i]) cout << u.first << " " << u.second << "\n";
// // cout << "\n\n";
}
signed main() {
cin >> n >> k;
for (int i = 0; i < n; i++) {
cin >> colours[i];
groups[colours[i]].push_back(i);
}
for (int i = 1; i < n; i++) {
cin >> p[i];
jmp[i][1] = p[i];
child[p[i]].push_back(i);
}
for (int k = 2; k < 21; k++) for (int i = 1; i < n; i++) jmp[i][k] = jmp[jmp[i][k-1]][k-1];
dfs(0,0);
find(0);
cout << best << " " << ans << "\n";
}
