/* 02.09.2025 */
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define fastIO ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
signed main(){
fastIO;
int n,k;cin>>n>>k;
vector<int> c(n);
vector<vector<int>> adj(n);
vector<int> tot(k);
for (int i = 0; i < n; ++i) {
cin >> c[i];
tot[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<unordered_map<int, int>> col_cnt(k);
vector<vector<int>> diff_depths(k);
auto dfs = [&](auto& dfs, int i, vector<int>& par) -> void {
int v = par[c[i]];
if (v == -1) {
is_root[i] = true;
} else {
col_adj[v].push_back(i);
}
par[c[i]] = i;
mx_depth[i] = depth[i];
col_cnt[c[i]][depth[i]]++;
diff_depths[c[i]].push_back(depth[i]);
for (auto& u : adj[i]) {
depth[u] = depth[i] + 1;
dfs(dfs, u, par);
mx_depth[i] = max(mx_depth[i], mx_depth[u]);
}
par[c[i]] = v;
};
vector<int> par(k, -1);
dfs(dfs, 0, par);
for (int i = 0; i < k; ++i) {
auto& v = diff_depths[i];
sort(begin(v), end(v));
v.erase(unique(begin(v), end(v)), end(v));
}
vector<map<int, int>> cnts(n);
map<int, int> curr_col;
int ans1=0,ans2=0;
const int M = sqrt(n);
auto dfs1 = [&](auto& dfs1, int i) -> void {
cnts[i][depth[i]] += 1;
for (auto& u : adj[i]) {
dfs1(dfs1, u);
if (cnts[i].size() < cnts[u].size()) swap(cnts[i], cnts[u]);
for (auto& [d, cnt] : cnts[u]) {
cnts[i][d] += cnt;
}
cnts[u].clear();
}
curr_col.clear();
if (is_root[i] && tot[c[i]] <= M) {
queue<int> q;
q.push(i);
while (q.size()) {
int v = q.front();
q.pop();
curr_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 : diff_depths[color]) {
if (cnts[i].count(d)) {
int space = cnts[i][d];
int can_get = min(space, col_cnt[color][d]);
now1 += can_get;
now2 += can_get - curr_col[d];
}
}
if (ans1 < now1) {
ans1 = now1;
ans2 = now2;
}
if (ans1 == now1) ans2 = min(ans2, now2);
}
};
dfs1(dfs1, 0);
cout<< ans1<<" "<<ans2<<'\n';
return 0;
vector<vector<int>> roots(k);
auto dfs2 = [&](auto& dfs2, int i, vector<int>& cnt, vector<int>& cur_col_cnt, int d, const int need) -> void {
while (d >= (int)cnt.size()) cnt.push_back(0);
while (d >= (int)cur_col_cnt.size()) cur_col_cnt.push_back(0);
cnt[d] += 1;
if (c[i] == need) cur_col_cnt[d]++;
for (auto& u : adj[i]) {
dfs2(dfs2, u, cnt, cur_col_cnt, d + 1, need);
}
};
for (int i = 0; i < n; ++i) {
if (is_root[i]) {
vector<int> cnt, cur_col_cnt;
dfs2(dfs2, i, cnt, cur_col_cnt, 0, c[i]);
cnt.push_back(0);
int d = 0;
int now1 = 0, now2 = 0;
while (cnt[d] > 0) {
int true_d = d + depth[i];
if (col_cnt[c[i]].count(true_d)) {
int can_get = min(cnt[d], col_cnt[c[i]][true_d]);
now1 += can_get;
now2 += can_get-cur_col_cnt[d];
}
d++;
}
if (ans1<now1) {
ans1=now1;
ans2=now2;
}
if (ans1==now1) ans2 = min(ans2,now2);
}
}
cout<<ans1<<" "<<ans2<<"\n";
}
