#include <bits/extc++.h>
using namespace std;
using namespace __gnu_pbds;
#define all(v) v.begin(), v.end()
const int M = 1e5 + 1, sq = 316;
vector<int> nei[M],pr[M];
cc_hash_table<int,int> dd[M],cnt[M],sp;
int dep[M],a[M],mxd[M],subt[M],st[M],en[M],t,gl;
vector<pair<int,int>> ans;
void init(int u)
{
st[u]=t++;
cnt[a[u]][dep[u]]++;
mxd[u]=dep[u],subt[u]=1;
for(int i:nei[u])
{
dep[i]=dep[u]+1;
init(i);
mxd[u]=max(mxd[i],mxd[u]);
subt[u]+=subt[i];
}
en[u]=t++;
}
void dfs1(int u)
{
if (nei[u].empty())
{
ans.push_back({1,0});
dd[u][dep[u]]++;
return;
}
int mx=nei[u][0];
for (int i:nei[u])
{
if (subt[i]>subt[mx])
mx=i;
dfs1(i);
}
swap(dd[u],dd[mx]);
dd[u][dep[u]]++;
for (int i:nei[u])
{
if (i!=mx)
for (auto [d,c]:dd[i])
dd[u][d]+=c;
}
if (pr[a[u]].size()>sq) return;
int x=0,y=0;
for (int i:pr[a[u]])
y+=(st[i]>=st[u] && st[i]<en[u]);
for (auto [w,h]:cnt[a[u]])
{
if (dd[u].find(w)!=dd[u].end())
x+=min(dd[u][w],h);
}
ans.push_back({x,x-y});
}
void dfs2(int u,int l)
{
if (a[u]==l) gl++;
sp[dep[u]]++;
for (int i:nei[u])
dfs2(i,l);
}
void dfs(int u,int l)
{
if (a[u]==l)
{
sp.clear(),gl=0;
dfs2(u,l);
int x=0;
for (auto [w,h]:sp)
{
if (cnt[l].find(w)!=cnt[l].end())
x+=min(cnt[l][w],h);
}
ans.push_back({x,x-gl});
}
for (int i:nei[u])
dfs(i,l);
}
int main()
{
ios::sync_with_stdio(0);
cin.tie(NULL), cout.tie(NULL);
int n,k;
cin>>n>>k;
for (int i=0;i<n;i++)
cin>>a[i],pr[a[i]].push_back(i);
for (int i=1;i<n;i++)
{
int p;
cin>>p;
nei[p].push_back(i);
}
init(0);
dfs1(0);
for (int l=0;l<k;l++)
{
if (pr[l].size()<=sq) continue;
dfs(0,l);
}
int x=0,y=0;
for (auto [p1,p2]:ans)
{
if (x<p1)
x=p1,y=p2;
if (x==p1)
y=min(y,p2);
}
cout<<x<<' '<<y<<endl;
return 0;
}
