#include <bits/stdc++.h>
using namespace std;
const int N=1e5+10;
vector<int> ma[N];
int h[N],sz[N],cnt[N],ans=0,color[N],cur_ans=0,n,k;
map<int,int> subtree[N],tree[N];
set<int> occur[N];
pair<int,int> maintain_ans[N];
pair<int,int> min_ans={0,0};
set<int> colors_maintain;
void dfs_sz(int x,int p=-1)
{
tree[h[x]][color[x]]++;
sz[x]=1;
occur[color[x]].insert(h[x]);
for(auto y:ma[x])
{
if(y==p)continue;
h[y]=h[x]+1;
dfs_sz(y,x);
sz[x]+=sz[y];
}
}
int req_color;
// ans_p+=subtree[h][color[x]];
// step_p+=min(cnt[h]-subtree[h][color[x]],tree[h][color[x]]-subtree[h][color[x]]);
void rem_contro(int he,int co)
{
maintain_ans[co].first-=subtree[he][co];
maintain_ans[co].second-=min(cnt[ he]-subtree[he][co],tree[he][co]-subtree[he][co]);
}
void add_contro(int he,int co)
{
maintain_ans[co].first+=subtree[he][co];
maintain_ans[co].second+=min(cnt[he]-subtree[he][co],tree[he][co]-subtree[he][co]);
}
void adder(int x,int p)
{
// color[i] < K
// if(color[x]<2)
for(auto col:colors_maintain)
{
rem_contro(h[x],col);
}
cnt[h[x]]++;
subtree[h[x]][color[x]]++;
for(auto col:colors_maintain)
{
add_contro(h[x],col);
}
for(auto y:ma[x])
{
if(y==p)continue;
adder(y,x);
}
}
void deleter(int x,int p)
{
// if(color[x]<2)
for(auto col:colors_maintain)
{
rem_contro(h[x],col);
}
cnt[h[x]]--;
subtree[h[x]][color[x]]--;
for(auto col:colors_maintain)
{
add_contro(h[x],col);
}
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);
}
// cur_ans=0;
for(auto col:colors_maintain)
{
maintain_ans[col]={0,0};
}
if(big!=-1)
{
dfs(big,x,1);
}
for(auto y:ma[x])
{
if(y==p or y==big)continue;
adder(y,x);
}
//Real solving part is this
// cnt[color[x]]++;
// ans=max(ans,cnt[color[x]]);
for(auto col:colors_maintain)
{
rem_contro(h[x],col);
}
cnt[h[x]]++;
subtree[h[x]][color[x]]++;
for(auto col:colors_maintain)
{
add_contro(h[x],col);
}
if(colors_maintain.find(color[x])!=colors_maintain.end())
{
min_ans=min(min_ans,{-maintain_ans[color[x]].first-maintain_ans[color[x]].second,maintain_ans[color[x]].second});
// min_ans=min(min_ans,{-maintain_ans[0].first-maintain_ans[0].second,maintain_ans[0].second});
// min_ans=min(min_ans,{-maintain_ans[1].first-maintain_ans[1].second,maintain_ans[1].second});
}
else
{
int ans_p=0,step_p=0;
// cout<<"NODe "<<x<<" caioo asL ";
// for(int h=1;h<=n;h++) // either iterate over all height where their is atleast one of color[x]s
for(int h:occur[color[x]]) // either iterate over all height where their is atleast one of color[x]s
{
ans_p+=subtree[h][color[x]];
// cout<<subtree[h][color[x]]<<' '<<h<<endl;
step_p+=min(cnt[h]-subtree[h][color[x]],tree[h][color[x]]-subtree[h][color[x]]);
// if(min(cnt[h]-subtree[h][color[x]],tree[h][color[x]]-subtree[h][color[x]])<0)cout<<"Error"<<endl;
}
min_ans=min(min_ans,{-ans_p-step_p,step_p});
}
// cout<<endl;
// if((ans_p+step_p)>4)
// {
// cout<<"Node "<<x<<' '<<-ans_p-step_p<<' '<<step_p<<endl;
// }
if(!keep)
{
deleter(x,p);
}
}
int main()
{
ios::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
cin>>n>>k;
for(int i=0;i<n;i++)cin>>color[i];
bool subtask=1;
for(int i=1;i<n;i++)
{
int x=i,y;
cin>>y;
subtask&=(y==(x-1));
// cout<<y<<' '<<x<<endl;
ma[y].push_back(x);
}
if(subtask)
{
map<int,int> apt;
int mx=0;
for(int i=n-1;i>=0;i--)
mx=max(mx,++apt[color[i]]);
cout<<mx<<' '<<0<<endl;
return 0;
}
h[0]=1;
dfs_sz(0);
const int SQ=300;
for(int i=0;i<k;i++)
{
if(occur[i].size()>SQ)
{
colors_maintain.insert(i);
maintain_ans[i]={0,0};
}
}
dfs(0);
cout<<-min_ans.first<<' '<<min_ans.second<<endl;
}
