#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
using namespace std;
#define inf 0x3F3F3F3F3F3F3F3F
#define bpc __builtin_popcountll
const int mod = 998244353;
const int MXN = 2e5 + 5;
const int RANDOM = chrono::high_resolution_clock::now().time_since_epoch().count();
struct chash {
int operator()(int x) const { return x ^ RANDOM; }
};
int n, k;
vector<int> adj[MXN];
int val[MXN], sz[MXN], dep[MXN], freq[MXN];
gp_hash_table<int, int, chash> mp[MXN], d[MXN];
gp_hash_table<int, gp_hash_table<int, int, chash>, chash> mp1[MXN];
array<int, 2> res = {0, 0};
void dfs(int a)
{
sz[a] = 1;
freq[val[a]]++;
for (int &v : adj[a])
{
dfs(v);
if (sz[a] < sz[v]) mp[a].swap(mp[v]), mp1[a].swap(mp1[v]);
for (auto it = mp1[v].begin(); it != mp1[v].end(); it++)
{
int key = (*it).first;
for (pair<int, int> p : (*it).second) mp1[a][key][p.first] += p.second;
}
for (auto &p : mp[v]) mp[a][p.first] += p.second;
sz[a] += sz[v];
}
freq[val[a]]--;
mp[a][dep[a]]++;
mp1[a][val[a]][dep[a]]++;
if (freq[val[a]]) return;
gp_hash_table<int, int, chash> &mp2 = mp1[a][val[a]];
array<int, 2> ans = {0, 0};
if (d[val[a]].size() < mp[a].size())
{
for (auto &p : d[val[a]]) ans[0] += min(p.second, mp[a][p.first]), ans[1] += min(p.second, mp[a][p.first]) - mp2[p.first];
}
else
{
for (auto &p : mp[a]) ans[0] += min(p.second, d[val[a]][p.first]), ans[1] += min(p.second, d[val[a]][p.first]) - mp2[p.first];
}
if (ans[0] > res[0]) res = ans;
else if (ans[0] == res[0]) res[1] = min(res[1], ans[1]);
}
void _init(int a)
{
d[val[a]][dep[a]]++;
for (int &v : adj[a])
{
dep[v] = dep[a] + 1;
_init(v);
}
}
signed main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
cin >> n >> k;
for (int i = 0; i < n; i++) cin >> val[i];
for (int i = 1; i < n; i++)
{
int p;
cin >> p;
adj[p].push_back(i);
}
_init(0);
dfs(0);
cout << res[0] << ' ' << res[1] << '\n';
}
