#include <bits/stdc++.h>
using namespace std;
const int N=1e6+10;
vector<int> ma[N];
int h[N],sz[N],cnt[N],ans=0,color[N];
void dfs_sz(int x,int p=-1)
{
sz[x]=1;
for(auto y:ma[x])
{
if(y==p)continue;
h[y]=h[x]+1;
dfs_sz(y,x);
sz[x]+=sz[y];
}
}
void adder(int x,int p)
{
cnt[color[x]]++;
for(auto y:ma[x])
{
if(y==p)continue;
adder(y,x);
}
}
void deleter(int x,int p)
{
cnt[color[x]]--;
for(auto y:ma[x])
{
if(y==p)continue;
deleter(y,x);
}
}
void dfs(int x,int p=-1,bool keep=0)
{
int big=-1;
for(auto y:ma[x])
{
if(y==p)continue;
if(big==-1 or sz[big]<sz[y])
big=y;
}
for(auto y:ma[x])
{
if(y==p or y==big)continue;
dfs(y,x);
}
if(big!=-1)
{
dfs(big,x,1);
}
for(auto y:ma[x])
{
if(y==p or y==big)continue;
adder(y,x);
}
cnt[color[x]]++;
ans=max(ans,cnt[color[x]]);
if(!keep)
{
deleter(x,p);
}
}
int main()
{
ios::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
int n,k;
cin>>n>>k;
for(int i=0;i<n;i++)cin>>color[i];
for(int i=1;i<n;i++)
{
int x=i,y;
cin>>y;
// ma[x].push_back(y);
ma[y].push_back(x);
}
h[0]=1;
dfs_sz(0);
dfs(0);
cout<<ans<<' '<<0<<endl;
}
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