#include <bits/stdc++.h>
using namespace std;
#ifdef LOCAL
#include "debug.h"
#else
#define dbg(...) 42
#endif
const int N = 1e5;
const int K = 1e5;
vector<int> g[N];
int a[N], p[N], cnt[N];
int depth[N];
set<int> d[N];
void build(int u, int p, int lvl = 0) {
depth[u] = lvl;
d[lvl].insert(u);
for (auto v : g[u]) {
if (v == p) continue;
build(v, u, lvl + 1);
}
}
set<int> b;
void dfs(int u, int p) {
b.insert(u);
for (auto v : g[u]) {
if (v == p) continue;
dfs(v, u);
}
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int n, k;
cin >> n >> k;
for (int i = 0; i < n; i++) {
cin >> a[i];
cnt[a[i]]++;
}
p[0] = -1;
for (int i = 1; i < n; i++) {
cin >> p[i];
g[i].push_back(p[i]);
g[p[i]].push_back(i);
}
if (n <= 2000) {
build(0, -1);
int mx = 1, mn = 0;
for (int u = 0; u < n; u++) {
b.clear();
dfs(u, p[u]);
int res = 0, swp = 0;
vector<int> c(n);
for (int i = 0; i < n; i++) {
for (auto v : d[i]) {
if (!b.count(v) && a[v] == a[u]) c[i]++;
}
}
vector<int> x(n), y(n);
for (auto v : b) {
if (a[u] == a[v]) {
res++;
x[depth[v]]++;
}
else {
y[depth[v]]++;
}
}
for (int i = depth[u] + 1; i < n; i++) {
res += min(y[i], c[i]);
swp += min(y[i], c[i]);
}
if (mx < res) {
mx = res;
mn = swp;
}
if (mx == res) {
mn = min(mn, swp);
}
}
cout << mx << ' ' << mn << '\n';
}
else {
int res = 0;
for (int i = 0; i < N; i++) res = max(res, cnt[i]);
cout << res << ' ' << 0 << '\n';
}
return 0;
}
