/* 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> current_col;
int ans1=0,ans2=0;
const int M=sqrt(n);
auto dfs1=[&](auto& dfs1,int i) -> void {
cnts[i][depth[i]]++;
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();
}
current_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();
current_col[depth[v]]++;
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 get=min(space, col_cnt[color][d]);
now1 =get;
now2+=get-current_col[d];
}
}
if (ans1<now1) {
ans1=now1;
ans2=now2;
}
if (ans1==now1) ans2=min(ans2,now2);
}
};
dfs1(dfs1,0);
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]++;
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] && tot[c[i]] > M) {
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 get=min(cnt[d], col_cnt[c[i]][true_d]);
now1+=get;
now2+=get-cur_col_cnt[d];
}
d++;
}
if (ans1<now1) {
ans1=now1;
ans2=now2;
}
if (ans1==now1) ans2=min(ans2,now2);
}
}
cout<<ans1<<' '<<ans2<<'\n';
return 0;
}
