#include <bits/stdc++.h>
using namespace std;
const int B = 300;
vector<int> bigColors; //colors with more than B people.
vector<int> anc; //the highest ancestor of each color.
vector<vector<int>> all; //all the people with each color.
vector<int> depth, maxDepth;
vector<int> cntDepth, cntColor;
vector<vector<int>> depthCol; //the number of nodes at each depth for the bigColors.
pair<int, int> ans = {0, 0};
void getDepth(int x, vector<vector<int>>& adj) {
maxDepth[x] = depth[x];
for (int node : adj[x]) {
depth[node] = depth[x] + 1;
getDepth(node, adj);
maxDepth[x] = max(maxDepth[x], maxDepth[node]);
}
}
void DFS(int x, vector<vector<int>>& adj, vector<int>& l) {
int c = l[x];
cntDepth[depth[x]]++;
cntColor[c]++;
if ((int)all[c].size() <= B) {
if (anc[c] == -1) {
anc[c] = x;
//I iterate over all of them.
int cntColorBefore = cntColor[c];
vector<int> before((int)all[c].size(), 0); //the number of nodes of each interesting depth before, i don't repeat depths.
for (int i = 0; i < (int)all[c].size(); i++) {
int y = all[c][i];
if (depth[y] <= depth[x] || (i > 0 && depth[y] == depth[all[c][i-1]])) continue;
before[i] = cntDepth[depth[y]];
}
for (int node : adj[x]) {
DFS(node, adj, l);
}
pair<int, int> res = {1, 0};
for (int i = 0; i < (int)all[c].size(); i++) {
int y = all[c][i];
if (depth[y] <= depth[x] || (i > 0 && depth[y] == depth[all[c][i-1]])) continue;
int total = cntDepth[depth[y]] - before[i]; //total #nodes with depth[y] in the subtree.
int numColor = 1; //total #node of color c with depth[y].
int mx = i;
for (int j = i+1; j < (int)all[c].size(); j++) {
if (depth[all[c][j]] == depth[y]) numColor++;
else break;
mx = j;
}
i = mx;
res.first += min(numColor, total);
}
res.second = res.first - 1 - (cntColor[c] - cntColorBefore);
if (res.first > ans.first) ans = res;
else if (res.first == ans.first) ans.second = min(ans.second, res.second);
anc[c] = -1;
} else {
for (int node : adj[x]) {
DFS(node, adj, l);
}
}
} else {
if (anc[c] == -1) {
anc[c] = x;
vector<int> before;
for (int i = depth[x]+1; i <= maxDepth[x]; i++) {
before.push_back(cntDepth[i]);
}
int cntColorBefore = cntColor[c];
for (int node : adj[x]) {
DFS(node, adj, l);
}
pair<int, int> res = {1, 0};
for (int i = depth[x] + 1; i <= maxDepth[x]; i++) {
int total = cntDepth[i] - before[i - (depth[x] + 1)];
int numColor = depthCol[c][i];
res.first += min(total, numColor);
}
res.second = res.first - 1 - (cntColor[c] - cntColorBefore);
if (res.first > ans.first) ans = res;
else if (res.first == ans.first) ans.second = min(ans.second, res.second);
anc[c] = -1;
} else {
for (int node : adj[x]) {
DFS(node, adj, l);
}
}
}
//I still have to update anc.
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
int N, K; cin >> N >> K;
vector<int> l(N);
all.resize(K);
for (int i = 0; i < N; i++) {
cin >> l[i];
all[l[i]].push_back(i);
}
for (int i = 0; i < K; i++) {
if ((int)all[i].size() > B) bigColors.push_back(i);
}
vector<vector<int>> adj(N);
for (int i = 1; i < N; i++) {
int p; cin >> p;
adj[p].push_back(i);
}
depth.assign(N, 0);
maxDepth.assign(N, 0);
getDepth(0, adj);
depthCol.resize(K);
for (int i = 0; i < K; i++) {
vector<pair<int, int>> nw;
for (int x : all[i]) nw.push_back({depth[x], x});
sort(nw.begin(), nw.end());
all[i].clear();
for (pair<int, int> pr : nw) all[i].push_back(pr.second);
if ((int)all[i].size() > B) {
depthCol[i].assign(N, 0);
for (int x : all[i]) depthCol[i][depth[x]]++;
}
}
anc.assign(K, -1);
cntDepth.assign(N, 0);
cntColor.assign(K, 0);
DFS(0, adj, l);
cout << ans.first << " " << ans.second << "\n";
}
