#include <bits/stdc++.h>
using namespace std;
#define int long long
#define fi first
#define se second
#define __builtin_popcount __builtin_popcountll
#define sz(v) ((int)(v).size())
#define mask(i) (1LL << (i))
#define getbit(mask, i) (((mask) >> (i)) & 1LL)
#define all(v) (v).begin(), (v).end()
template<typename X> void db(X x) { cerr << x << "] "; }
template<typename X, typename ...Y> void db(X x, Y... y) { cerr << x << ", "; db(y...); }
#define debug(...) cerr << "[" << #__VA_ARGS__ << ": ", db(__VA_ARGS__), cerr << "\n";
template <class T1, class T2> bool maximize(T1 &a, T2 &b) { return a < b ? a = b, 1 : 0; }
template <class T1, class T2> bool minimize(T1 &a, T2 &b) { return a > b ? a = b, 1 : 0; }
#define TASK "code"
void solve();
signed main() {
ios_base::sync_with_stdio(false);cin.tie(nullptr);cout.tie(nullptr);
// if (fopen(TASK".inp", "r")) {
// freopen(TASK".inp", "r", stdin);
// freopen(TASK".out", "w", stdout);
// }
int tc = 1, d = 0;
// cin >> tc;
while(tc--) {
++d;
// cout << "Case #" << d << ": ";
solve();
}
return 0;
}
const int mod = 1e9 + 7;
const int inf = 1e18;
const int N = 2e5 + 5;
int n, k;
int h[N], col[N];
vector <int> adj[N];
vector <int> ds[N];
vector <int> a[N];
namespace sub34 {
const int MAXL = 1e5;
int id[N], tin[N], cnt[N];
int timer;
pair <int, int> ans = {-1, 0};
void Max(pair<int, int> &a, pair <int, int> b) {
if(a.fi < b.fi) a = b;
else if(a.fi == b.fi) a.se = min(a.se, b.se);
}
void dfs(int u, int p) {
id[u] = tin[u] = ++timer;
for (auto v : adj[u]) if(v != p) {
h[v] = h[u] + 1;
dfs(v, u);
id[u] = id[v];
}
}
void dfs1(int u, int p) {
for (auto v : adj[u]) if(v != p) {
dfs1(v, u);
if(sz(a[u]) < sz(a[v])) {
swap(a[u], a[v]);
}
for (int i = sz(a[v]) - 1, j = sz(a[u]) - 1; i >= 0; i--, j--) {
a[u][j] += a[v][i];
}
}
a[u].push_back(1);
if (sz(ds[col[u]]) <= MAXL) {
int c = 0, k = 0;
for (auto v : ds[col[u]]) {
int d = sz(a[u]) - 1 - (h[v] - h[u]);
k += (tin[v] >= tin[u] && tin[v] <= id[u]);
if (d >= 0 && d < sz(a[u]) && cnt[d] < a[u][d]) {
cnt[d]++, c++;
}
}
Max(ans, {c, c - k});
for (auto v : ds[col[u]]) {
int d = sz(a[u]) - 1 - (h[v] - h[u]);
if (d >= 0 && d < sz(a[u])) cnt[d] = 0;
}
}
}
void solve() {
dfs(1, 0); dfs1(1, 0);
cout << ans.fi << ' ' << ans.se;
}
}
namespace sub1 {
int cnt[N];
void solve() {
for (int i = 1; i <= n; ++i) {
cnt[col[i]]++;
}
int ans = 0;
for (int i = 0; i < k; ++i) ans = max(ans, cnt[i]);
cout << ans << " 0\n";
}
}
void solve() {
cin >> n >> k;
for (int i = 1; i <= n; ++i) {
cin >> col[i];
ds[col[i]].push_back(i);
}
bool checksub1 = 1;
for (int i = 2; i <= n; ++i) {
int u;
cin >> u;
++u;
if(u != i - 1) checksub1 = 0;
adj[i].push_back(u);
adj[u].push_back(i);
}
if(checksub1) return sub1::solve(), void();
sub34::solve();
}
