#include <bits/stdc++.h>
using namespace std;
using ll = long long;
int main() {
ios::sync_with_stdio(0);
cin.tie(0);
int n, k;
cin >> n >> k;
vector<int> c(n);
vector<vector<int>> adj(n);
for (int i = 0; i < n; ++i) {
cin >> c[i];
}
for (int i = 1; i < n; ++i) {
int x;
cin >> x;
adj[x].push_back(i);
}
vector<bool> is_root(n);
vector<vector<int>> col_adj(n);
vector<int> depth(n), mx_depth(n);
vector<map<int, int>> col_count(k);
auto dfs = [&](auto& dfs, int i, vector<int>& parent) -> void {
int prv_c = parent[c[i]];
if (prv_c == -1) {
is_root[i] = true;
} else {
col_adj[prv_c].push_back(i);
}
parent[c[i]] = i;
mx_depth[i] = depth[i];
col_count[c[i]][depth[i]]++;
for (auto& u : adj[i]) {
depth[u] = depth[i] + 1;
dfs(dfs, u, parent);
mx_depth[i] = max(mx_depth[i], mx_depth[u]);
}
parent[c[i]] = prv_c;
};
vector<int> parent(k, -1);
dfs(dfs, 0, parent);
//~ for (int i = 0; i < n; ++i) {
//~ cout << is_root[i] << " ";
//~ }
//~ cout << "\n";
vector<map<int, int>> counts(n);
int res1 = 0, res2 = 0;
auto dfs1 = [&](auto& dfs1, int i) -> void {
counts[i][depth[i]] += 1;
for (auto& u : adj[i]) {
dfs1(dfs1, u);
if (counts[i].size() < counts[u].size()) swap(counts[i], counts[u]);
for (auto& [d, cnt] : counts[u]) {
counts[i][d] += cnt;
}
}
map<int, int> current_col;
if (is_root[i]) {
queue<int> q;
q.push(i);
while (q.size()) {
int v = q.front();
q.pop();
current_col[depth[v]] += 1;
for (auto& u : col_adj[v]) {
q.push(u);
}
}
int now1 = 0, now2 = 0;
const int color = c[i];
for (auto& [d, space] : counts[i]) {
int can_get = min(space, col_count[color][d]);
now1 += can_get;
assert(can_get >= current_col[d]);
now2 += can_get - current_col[d];
}
if (res1 < now1) {
res1 = now1;
res2 = now2;
}
if (res1 == now1) res2 = min(res2, now2);
}
};
dfs1(dfs1, 0);
cout << res1 << " " << res2 << "\n";
}
