#include <bits/stdc++.h>
using namespace std;
#define pp pair <int, int>
#define fi first
#define se second
#define yes cout << "YES\n"
#define no cout << "NO\n"
const int N = 3e5 + 9;
const int blocksz = 320;
int n, k, c[N];
int h[N], sz[N];
int max_depth = 0;
int in[N], out[N], timedfs = 0;
int tour[N];
vector <int> adj[N];
vector <int> pos[N];
vector <int> large, small;
int mark[N];
pp res = {1LL, 0LL};
pp cmp (pp A, pp B){
if (A.fi > B.fi) return A;
if (A.fi < B.fi) return B;
if (A.se <= B.se) return A;
return B;
}
void dfs (int u){
tour[++timedfs] = u;
in[u] = timedfs;
max_depth = max (max_depth, h[u]);
for (int v : adj[u]){
h[v] = h[u] + 1;
dfs (v);
}
out[u] = timedfs;
}
int cur_color;
int cnt_color[N];
int num[N];
int cnt[N];
void dfs_color (int u){
if (c[u] == cur_color){
cnt_color[h[u]]++;
cnt[u]++;
}
for (int v : adj[u]){
dfs_color (v);
cnt[u] += cnt[v];
}
}
int mp[N];
pp temp_ans;
void dfs4 (int u){
if (mp[h[u]] < cnt_color[h[u]]) temp_ans.fi++;
mp[h[u]]++;
for (int v : adj[u]) dfs4 (v);
}
void dfs3 (int u){
if (c[u] == cur_color){
temp_ans.fi = 0;
dfs4 (u);
temp_ans.se = cnt[u] - temp_ans.fi;
temp_ans.se = -temp_ans.se;
res = cmp (res, temp_ans);
for (int i = h[u]; i <= max_depth; i++) mp[i] = 0;
return;
}
for (int v : adj[u]) dfs3 (v);
}
void solve_large (int color){
cur_color = color;
memset (cnt, 0, sizeof (cnt));
memset (cnt_color, 0, sizeof (cnt_color));
dfs_color (1);
dfs3 (1);
}
vector <int> L[N];
void dfs_merge (int u){
if (adj[u].size () == 0){
pos[u].push_back (1);
return;
}
for (int v : adj[u]){
dfs_merge (v);
if (pos[v].size () > pos[u].size ()) swap (pos[u], pos[v]);
for (int z = 0; z < pos[v].size (); z++){
if (z >= pos[u].size ()) pos[u].push_back (0);
pos[u][z] += pos[v][z];
}
pos[v].clear ();
}
pos[u].insert (pos[u].begin (), 1);
temp_ans.fi = temp_ans.se = 0;
for (int i = 0; i < L[c[u]].size (); i++){
int x = L[c[u]][i];
if (h[x] < h[u]) continue;
int cnt_node = 1;
int in_subtree = 0;
int j = i + 1;
if (in[u] <= in[x] && in[x] <= out[u]) in_subtree = 1;
while (j < L[c[u]].size () && h[L[c[u]][j]] == h[x]){
cnt_node++;
int y = L[c[u]][j];
if (in[u] <= in[y] && in[y] <= out[u]) in_subtree++;
j++;
if (j >= L[c[u]].size ()) break;
}
if (h[x] - h[u] < pos[u].size () && h[x] - h[u] >= 0){
temp_ans.fi += min (cnt_node, pos[u][h[x] - h[u]]);
temp_ans.se += min (cnt_node, pos[u][h[x] - h[u]]) - in_subtree;
}
i = j - 1;
}
res = cmp (res, temp_ans);
}
bool cmp_depth (int u, int v){
return h[u] < h[v];
}
void solve_small (){
for (int i = 1; i <= n; i++){
if (mark[c[i]] == 0) continue;
L[c[i]].push_back (i);
}
for (int i = 0; i < k; i++) if (L[i].size ()) sort (L[i].begin (), L[i].end (), cmp_depth);
dfs_merge (1);
}
signed main (){
ios_base::sync_with_stdio (false);
cin.tie(0); cout.tie(0);
cin >> n >> k;
for (int i = 1; i <= n; i++){
cin >> c[i];
sz[c[i]]++;
}
for (int i = 0; i < k; i++){
if (sz[i] >= blocksz) large.push_back (i);
else if (sz[i]){
small.push_back (i);
mark[i]++;
}
}
for (int i = 2, p; i <= n; i++){
cin >> p; p++;
adj[p].push_back (i);
}
dfs (1);
for (int i : large) solve_large (i);
solve_small ();
cout << res.fi << ' ' << res.se;
}
