#include <bits/stdc++.h>
using namespace std;
#define iter(v) v.begin(), v.end()
#define pb emplace_back
#define ff first
#define ss second
#define SZ(v) int(v.size())
using ll = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
#ifdef zisk
void debug() { cerr << "\n"; }
template<class T, class ... U>
void debug(T a, U... b) {
cerr << a << " ", debug(b...);
}
template<class T>
void pary(T l, T r){
while (l != r) cerr << *l << " ", l++;
cerr << "\n";
}
#else
#define debug(...) void()
#define pary(...) void()
#endif
int main() {
ios_base::sync_with_stdio(false);
cin.tie(0);
int n, K;
cin >> n >> K;
const int B = 400;
vector<int> color(n);
vector<vector<int>> pos(K);
for (int i = 0; i < n; i++) {
cin >> color[i];
pos[color[i]].pb(i);
}
vector<vector<int>> g(n);
for (int i = 1; i < n; i++) {
int p;
cin >> p;
g[p].pb(i);
}
vector<int> dpt(n), in(n), out(n);
int ts = 0;
vector<int> cur(K, -1);
vector<bool> top(n);
auto dfs1 = [&](auto dfs, int now) -> void {
in[now] = ts++;
if (cur[color[now]] == -1) {
cur[color[now]] = now;
top[now] = true;
}
for (int i : g[now]) {
dpt[i] = dpt[now] + 1;
dfs(dfs, i);
}
if (cur[color[now]] == now)
cur[color[now]] = -1;
out[now] = ts++;
};
dfs1(dfs1, 0);
auto isAnc = [&](int a, int b) {
return in[a] <= in[b] && out[b] <= out[a];
};
int ans_member = 0, ans_swp = 0;
auto solve_big = [&](int c) {
//debug("solve_big", c);
vector<int> total(n + 1);
for (int i = 0; i < n; i++)
if (color[i] == c) total[dpt[i]]++;
vector<int> cnt(n + 1), sz(n + 1);
auto dfs2 = [&](auto dfs, int now, int type) -> void {
sz[dpt[now]] += type;
if (color[now] == c) cnt[dpt[now]] += type;
for (int i : g[now]) dfs(dfs, i, type);
};
for (int i = 0; i < n; i++)
if (color[i] == c && top[i]) {
dfs2(dfs2, i, 1);
int member = 0, swp = 0;
for (int j = dpt[i]; j <= n && sz[j]; j++) {
//debug("depth", j, sz[j], cnt[j], total[j]);
int tmp = min(total[j], sz[j]);
member += tmp;
swp += tmp - cnt[j];
}
//debug("top", i, member, swp);
if (member > ans_member) ans_member = member, ans_swp = swp;
else if (member == ans_member && swp < ans_swp) ans_swp = swp;
dfs2(dfs2, i, -1);
}
};
for (int i = 0; i < K; i++)
if (SZ(pos[i]) > B)
solve_big(i);
{
vector<deque<int>> down(n);
vector<int> total(n), cnt(n);
vector<bool> vst(n);
auto dfs3 = [&](auto dfs, int now) -> void {
down[now].pb(1);
for (int i : g[now]) {
dfs(dfs, i);
down[i].emplace_front(0);
if (SZ(down[i]) > SZ(down[now]))
down[now].swap(down[i]);
for (int j = 0; j < SZ(down[i]); j++)
down[now][j] += down[i][j];
}
//debug("dfs3", now);
//pary(iter(down[now]));
if (SZ(pos[color[now]]) > B) return;
for (int i : pos[color[now]]) {
total[dpt[i]]++;
if (isAnc(now, i)) cnt[dpt[i]]++;
}
int member = 0, swp = 0;
for (int i : pos[color[now]]) {
int d = dpt[i];
if (vst[d]) continue;
vst[d] = true;
if (d < dpt[now] || d >= dpt[now] + SZ(down[now])) continue;
int tmp = min(total[d], down[now][d - dpt[now]]);
member += tmp;
swp += tmp - cnt[d];
}
if (member > ans_member) ans_member = member, ans_swp = swp;
else if (member == ans_member && swp < ans_swp) ans_swp = swp;
for (int i : pos[color[now]]) {
int d = dpt[i];
total[d] = 0;
cnt[d] = 0;
vst[d] = false;
}
};
dfs3(dfs3, 0);
}
cout << ans_member << " " << ans_swp << "\n";
}
