#include <iostream>
#include <math.h>
#include <vector>
#include <string>
#include <algorithm>
#include <queue>
#include <stack>
#include <map>
#include <cstring>
#include <iomanip>
#include <set>
#include <bitset>
#include <unordered_map>
#define int long long
using namespace std;
using ll = long long;
using pii = pair<int,int>;
using piii = tuple<int,int,int>;
#define f first
#define s second
#define endl '\n'
#define all(x) begin(x),end(x)
int const N = 2e5+10;
int const INF = 1e18+10;
int val[N];
map<int,int> depthcnt[N];//color -> depth,amount
vector<int> adj[N];
int depth[N];
int nodecnt[N];
map<int,int> curcnt[N];//color -> amount of stuff of in n depth in current subtree
int fullcnt[N];//amount of stuff of in n depth in current subtree
int intime[N];
int outtime[N];
int rtime[N];
pii ans = {-INF,INF};
int t = 0;
void dfs(int n){
nodecnt[n] = 1;
if(!depthcnt[val[n]].count(depth[n])) depthcnt[val[n]][depth[n]] = 0;
depthcnt[val[n]][depth[n]]++;
intime[n] = t++;
rtime[intime[n]] = n;
for(auto k:adj[n]){
depth[k] = depth[n]+1;
dfs(k);
nodecnt[n] += nodecnt[k];
}
outtime[n] = t;
}
void manage(int n,int func){
for(int i{intime[n]};i < outtime[n];i++){
int k = rtime[i];
if(func) curcnt[val[k]][depth[k]]++;
else curcnt[val[k]][depth[k]]--;
}
for(int i{intime[n]};i < outtime[n];i++){
int k = rtime[i];
if(func) fullcnt[depth[k]]++;
else fullcnt[depth[k]]--;
}
}
pii findans(int c){
pii ans = {0,0};
for(auto [a,b]:depthcnt[c]){
int val = min(fullcnt[a],b);
ans.f += val;
ans.s += val-curcnt[c][a];
}
return ans;
}
void sack1(int n,int keep){
pii hv = {0,-1};
for(auto k:adj[n]) hv = max(hv,{nodecnt[k],k});
for(auto k:adj[n]) if(k != hv.s) sack1(k,0);
if(hv.s != -1) sack1(hv.s,1);
for(auto k:adj[n]) if(k != hv.s) manage(k,1);
curcnt[val[n]][depth[n]]++;
fullcnt[depth[n]]++;
auto ret = findans(val[n]);
ans = max(ans,{ret.f,-ret.s});
//cout << n << " " << ret.f << " " << ret.s << endl;
if(!keep) manage(n,0);
}
signed main(){
ios_base::sync_with_stdio(0);cin.tie(0);
int n;cin >> n;
int k;cin >> k;
for(int i{};i < n;i++){
cin >> val[i];
}
for(int i{1};i < n;i++){
int g;cin >> g;
adj[g].emplace_back(i);
}
dfs(0);
// for(int i{};i < k;i++){
// for(auto [a,b]:depthcnt[i]) cout << a << "-" << b << " ";
// cout << endl;
// }
sack1(0,0);
cout << ans.f << " " << -ans.s;
}
