#include <bits/stdc++.h>
using namespace std;
#define all(v) v.begin(), v.end()
const int M = 1e5 + 1;
vector<int> nei[M],ver[M];
int dep[M],st[M],en[M],t;
void dfs(int u)
{
st[u]=t++;
ver[dep[u]].push_back(st[u]);
for (int i:nei[u])
dep[i]=dep[u]+1,dfs(i);
en[u]=t++;
}
int main()
{
int n,k;
cin>>n>>k;
vector<int> v[k];
for (int i=0;i<n;i++)
{
int x;
cin>>x;
v[x].push_back(i);
}
for (int i=1;i<n;i++)
{
int p;
cin>>p;
nei[p].push_back(i);
}
dfs(0);
int ans=0,s=0;
for (int l=0;l<k;l++)
{
for (int u:v[l])
{
map<int,int> cnt,tot;
int x=1,y=0;
for (int j:v[l])
{
if (dep[j]<=dep[u]) continue;
if (tot.find(dep[j])==tot.end())
tot[dep[j]]=lower_bound(all(ver[dep[j]]),en[u])-lower_bound(all(ver[dep[j]]),st[u]);
if (st[j]>st[u] && st[j]<en[u])
x++,tot[dep[j]]--;
else
cnt[dep[j]]++;
}
for (auto [d,c]:cnt)
x+=min(c,tot[d]),y+=min(c,tot[d]);
if (x>ans)
ans=x,s=y;
else if(x==ans)
s=min(s,y);
}
}
cout<<ans<<' '<<s<<endl;
return 0;
}
