#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define sz(x) (int)size(x)
#define all(x) (x).begin(), (x).end()
vector<int> color;
vector<map<int, int>> colByD;
vector<vector<int>> g;
vector<vector<int>> layerSz;
vector<int> cntAbove, cntTotal;
int maxCnt = 0, minSwaps = 0;
void dfs(int u, int par, int d){
cntAbove[color[u]]++;
int cntAlready = -cntTotal[color[u]];
cntTotal[color[u]]++;
for(int v : g[u]){
if(v == par) continue;
dfs(v, u, d+1);
if(sz(layerSz[v]) > sz(layerSz[u])) swap(layerSz[u], layerSz[v]);
for(int i = 0; i < sz(layerSz[v]); i++) layerSz[u][sz(layerSz[u])-sz(layerSz[v])+i] += layerSz[v][i];
}
layerSz[u].push_back(1);
cntAbove[color[u]]--;
cntAlready += cntTotal[color[u]];
if(cntAbove[color[u]] == 0){
auto it = colByD[color[u]].lower_bound(d);
int cnt = 0;
while(it != colByD[color[u]].end()){
int i = sz(layerSz[u])-1 + d - it->first;
if(i < 0) break;
cnt += min(layerSz[u][i], it->second);
it++;
}
if(cnt > maxCnt){
maxCnt = cnt;
minSwaps = cnt - cntAlready;
}
else if(cnt == maxCnt) minSwaps = min(minSwaps, cnt - cntAlready);
}
}
void solve(){
int n, k;
cin >> n >> k;
color.resize(n);
for(int &e : color) cin >> e;
g.resize(n);
for(int i = 1; i < n; i++){
int x;
cin >> x;
g[x].push_back(i);
}
colByD.resize(n);
auto dfsDepth = [&](auto&& self, int u, int par, int d) -> void {
colByD[color[u]][d]++;
for(int v : g[u]){
if(v == par) continue;
self(self, v, u, d+1);
}
};
dfsDepth(dfsDepth, 0, -1, 0);
layerSz.resize(n);
cntAbove.resize(k);
cntTotal.resize(k);
dfs(0, -1, 0);
cout << maxCnt << " " << minSwaps << "\n";
}
int main(){
cin.tie(0)->sync_with_stdio(false);
solve();
}
