//----------vahagng----------//
#define _CRT_SECURE_NO_WARNINGS
#include <bits/stdc++.h>
// #include <ext/pb_ds/assoc_container.hpp>
using namespace std;
// using namespace __gnu_pbds;
// template <class T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
#ifndef ONLINE_JUDGE
#define dbg(x) cerr << #x <<" "; print(x); cerr << endl;
#else
#define dbg(x)
#endif
void print(long long t) { cerr << t; }
void print(int t) { cerr << t; }
void print(string t) { cerr << t; }
void print(char t) { cerr << t; }
void print(double t) { cerr << t; }
void print(long double t) { cerr << t; }
void print(unsigned long long t) { cerr << t; }
template <class T, class V> void print(pair <T, V> p);
template <class T> void print(vector <T> v);
template <class T> void print(set <T> v);
template <class T, class V> void print(map <T, V> v);
template <class T> void print(multiset <T> v);
template <class T, class V> void print(T v[], V n) { cerr << "["; for (int i = 0; i < n; i++) { cerr << v[i] << " "; } cerr << "]"; }
template <class T, class V> void print(pair <T, V> p) { cerr << "{"; print(p.first); cerr << ","; print(p.second); cerr << "}"; }
template <class T> void print(vector <T> v) { cerr << "[ "; for (T i : v) { print(i); cerr << " "; } cerr << "]"; }
template <class T> void print(set <T> v) { cerr << "[ "; for (T i : v) { print(i); cerr << " "; } cerr << "]"; }
template <class T> void print(multiset <T> v) { cerr << "[ "; for (T i : v) { print(i); cerr << " "; } cerr << "]"; }
template <class T, class V> void print(map <T, V> v) { cerr << "[ "; for (auto i : v) { print(i); cerr << " "; } cerr << "]"; }
#define ll long long
#define all(v) v.begin(), v.end()
#define rall(v) v.rbegin(), v.rend()
#define ld long double
#define sz(v) v.size()
#define endl '\n'
const ll inf = 2e18, mod = 1e9 + 7, mod2 = 998244353;
void SetIO(string str = "") {
if (str != "") {
freopen((str + ".in").c_str(), "r", stdin);
freopen((str + ".out").c_str(), "w", stdout);
}
else {
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
}
}
void FastIO() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
cout.tie(nullptr);
}
const int N = 3e5 + 10, M = 1e7 + 10;
mt19937 rnd(chrono::system_clock::now().time_since_epoch().count());
ll binpow(ll a, ll b) {
ll res = 1;
while (b) {
if (b & 1) {
res = (res * a) % mod2;
}
b >>= 1;
a = (a * a) % mod2;
}
return res;
}
ll n, k, p[N], a[N], c[N], tin[N], tout[N], timer, dp[2002][2002], depth[N];
vector<int> adj[N], H[2001][2002];
void dfs0(int node, int parent, int d) {
H[d][a[node]].push_back(node);
depth[node] = d;
tin[node] = ++timer;
dp[node][a[node]] = 1;
for (auto i : adj[node]) {
if (i == parent) continue;
dfs0(i, node, d + 1);
for (int j = 0; j < k; j++) {
dp[node][j] += dp[i][j];
}
}
tout[node] = timer;
}
int cur;
void dfs(int node, int parent, int d, int lang, int root) {
int k = 0;
for (auto i : adj[node]) {
if (i == parent) continue;
if (a[i] != lang) k++;
}
int C = 0;
for (auto i : H[d + 1][lang]) {
if (!(tin[root] <= tin[i] && tout[root] >= tout[i])) {
dbg(root);
dbg(i);
C++;
}
}
// dbg(lang);
// dbg(d);
// dbg(H[d + 1][lang]);
cur += min(C, k);
for(auto i : adj[node]){
if (i == parent) continue;
dfs(i, node, d + 1, lang, root);
}
}
void solve(int tc) {
cin >> n >> k;
for (int i = 1; i <= n; i++) {
cin >> a[i];
c[a[i]]++;
}
bool flag = 1;
for (int i = 2; i <= n; i++) {
cin >> p[i];
p[i]++;
flag &= (p[i] == i - 1);
adj[p[i]].push_back(i);
adj[i].push_back(p[i]);
}
if (flag) {
cout << *max_element(c, c + k) << ' ' << 0 << endl;
return;
}
dfs0(1, 0, 0);
int ans = 0, ans_sw = 2*n;
for (int i = 1; i <= n; i++) {
cur = 0;
dfs(i, p[i], depth[i], a[i], i);
int C = cur + dp[i][a[i]];
if (C > ans) {
ans = C;
ans_sw = cur;
}
else if (C == ans && cur < ans_sw) {
ans_sw = cur;
}
}
cout << ans << ' ' << ans_sw << endl;
}
void precalc() {
}
int main() {
// SetIO("teamwork");
FastIO();
int test_case = 1;
// cin >> test_case;
precalc();
int cnt = 1;
while (test_case--) {
solve(cnt++);
}
return 0;
}
