#include <bits/stdc++.h>
#define pi pair<int, int>
using namespace std;
const int MAXN = 200005;
int n, k;
int col[MAXN];
vector<vector<int>> adj;
vector<vector<int>> colorCnt;
pair<int, int> res = {0, 0};
void dfs1(int v, int level, vector<int>& vertices) {
stack<pi> s;
s.push({v, level});
while (!s.empty()) {
tie(v, level) = s.top();
s.pop();
vertices[level]++;
for (int to : adj[v]) {
s.push({to, level + 1});
}
}
}
void dfs2(int v, int level, vector<vector<int>>& colorCnt) {
stack<pi> s;
s.push({v, level});
while (!s.empty()) {
tie(v, level) = s.top();
s.pop();
colorCnt[level][col[v]]++;
for (int to : adj[v]) {
s.push({to, level + 1});
}
}
}
int dfs3(int v, int c) {
int res = 0;
if (col[v] == c) res++;
for (int to : adj[v]) {
res += dfs3(to, c);
}
return res;
}
void dfs(int v, int level, const vector<vector<int>>& colorCnt) {
int c = col[v];
vector<int> vertices(n, 0);
dfs1(v, level, vertices);
int coders = 0, swaps = 0;
for (int l = level + 1; l < n; l++) {
coders += min(vertices[l], colorCnt[l][c]);
}
swaps = (coders + 1) - dfs3(v, c);
if (coders > res.first || (coders == res.first && swaps < res.second)) {
res = {coders, swaps};
}
for (int to : adj[v]) {
dfs(to, level + 1, colorCnt);
}
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
cin >> n >> k;
for (int i = 0; i < n; ++i) {
cin >> col[i];
}
adj.assign(n, vector<int>());
for (int i = 1; i < n; ++i) {
int x;
cin >> x;
adj[x].push_back(i);
}
colorCnt.assign(n, vector<int>(k, 0));
dfs2(0, 0, colorCnt);
dfs(0, 0, colorCnt);
cout << res.first + 1 << " " << res.second << "\n";
return 0;
}
