#include<bits/stdc++.h>
typedef long long ll;
#define pb push_back
#define fr first
#define sc second
#define endl '\n'
using namespace std;
#define mid ((left+right)>>1)
int s=317;
int n,k;
int arr[100023];
vector<int>renk[100023],deps[100023];
vector<int>child[100023];
int in[100023],out[100023];
int dep[100023],h[100023];
int tim=0;
pair<int,int>res[100023];
pair<int,int>ans;
void dfs(int pos){
in[pos]=++tim;
deps[dep[pos]].pb(pos);
for(int x:child[pos]){
dep[x]=dep[pos]+1;
dfs(x);
h[pos]=max(h[pos],h[x]+1);
}
out[pos]=tim;
}
int main(){
ios_base::sync_with_stdio(23^23);cin.tie(NULL);
cin>>n>>k;
ans={-1,0};
for(int i=1;i<=n;i++){
res[i]={-1,0};
cin>>arr[i];
arr[i]++;
renk[arr[i]].pb(i);
}
for(int i=2;i<=n;i++){
int x;cin>>x;x++;
child[x].pb(i);
}
dfs(1);
for(int o=1;o<=k;o++){
if(!renk[o].size())continue;
if(renk[o].size()>s){
sort(renk[o].begin(),renk[o].end(),[&](const int &x,const int &y){
return in[x]<in[y];
});
vector<int>roots;
vector<int>pot;
int mxout=0;
for(int x:renk[o]){
if(in[x]>mxout){
pot.pb(x);
}
mxout=max(mxout,out[x]);
}
sort(pot.begin(),pot.end(),[&](const int &x,const int &y){
return dep[x]+h[x]<dep[y]+h[y];
});
for(int i=n-1;i>0;i--){
vector<int>roots2;
for(int j=0;j<roots.size();j++){
int x=roots[j];
if(dep[x]<i)roots2.pb(x);
}
swap(roots,roots2);
int cnt=0;
vector<int>v;
for(int x:deps[i]){
if(arr[x]==o){
cnt++;
v.pb(x);
}
}
while(pot.size()&&dep[pot.back()]+h[pot.back()]>=i){
roots.pb(pot.back());
pot.pop_back();
}
for(int j=0;j<roots.size();j++){
int var=0;
int top=0;
int l2=0,r2=deps[i].size();
while(l2<r2){
int mi=(l2+r2)/2;
int x=deps[i][mi];
if(in[x]>=in[roots[j]])r2=mi;
else l2=mi+1;
}
top-=l2;
l2=0;r2=deps[i].size();
while(l2<r2){
int mi=(l2+r2)/2;
int x=deps[i][mi];
if(in[x]>out[roots[j]])r2=mi;
else l2=mi+1;
}
top+=l2;
l2=0;r2=v.size();
while(l2<r2){
int mi=(l2+r2)/2;
int x=v[mi];
if(in[x]>=in[roots[j]])r2=mi;
else l2=mi+1;
}
var-=l2;
l2=0;r2=v.size();
while(l2<r2){
int mi=(l2+r2)/2;
int x=v[mi];
if(in[x]>out[roots[j]])r2=mi;
else l2=mi+1;
}
var+=l2;
res[roots[j]].fr-=min(top,cnt);
res[roots[j]].sc+=max(0,min(top-var,cnt-var));
ans=min(ans,res[roots[j]]);
}
}
}
else{
sort(renk[o].begin(),renk[o].end(),[&](const int &x,const int &y){
return dep[x]<dep[y];
});
vector<int>v;
for(int i=0;i<renk[o].size();i++){
for(int j=i+1;j<renk[o].size();j++){
if(dep[renk[o][j]]<=dep[renk[o][i]])continue;
v.pb(renk[o][j]);
if(j+1==renk[o].size()||dep[renk[o][j+1]]!=dep[renk[o][j]]){
int var=0,top=0;
int cnt=v.size();
for(int x:v){
if(in[x]>=in[renk[o][i]]&&in[x]<=out[renk[o][i]])var++;
}
int l=0,r=deps[dep[v.back()]].size();
while(l<r){
int mi=(l+r)/2;
int x=deps[dep[v.back()]][mi];
if(in[x]>=in[renk[o][i]])r=mi;
else l=mi+1;
}
top-=l;
l=0;r=deps[dep[v.back()]].size();
while(l<r){
int mi=(l+r)/2;
int x=deps[dep[v.back()]][mi];
if(in[x]>out[renk[o][i]])r=mi;
else l=mi+1;
}
top+=l;
res[renk[o][i]].fr-=min(top,cnt);
res[renk[o][i]].sc+=max(0,min(top-var,cnt-var));
v.clear();
}
}
//cout<<renk[o][i]<<": "<<-res[renk[o][i]].fr<<" "<<res[renk[o][i]].sc<<endl;
ans=min(ans,res[renk[o][i]]);
}
}
}
cout<<-ans.fr<<" "<<ans.sc<<endl;
}
