#include <bits/stdc++.h>
using namespace std;
#define forn(i,n) for(int i=0;i<int(n);i++)
#define forsn(i,s,n) for(int i=int(s);i<int(n);i++)
#define dforn(i,n) for(int i=int(n)-1;i>=0;i--)
#define dforsn(i,s,n) for(int i=int(n)-1;i>=int(s);i--)
#define fst first
#define snd second
#define pb push_back
#define eb emplace_back
#define sz(x) (int)x.size()
#define all(x) x.begin(), x.end()
typedef long long ll;
typedef vector<ll> vll;
typedef vector<int> vi;
typedef pair<int,int> ii;
const int N=1e5+9;
int l[N];
vi adj[N];
unordered_map<int, int> cnt[N];
vi vals[N];
void dfs0(int u, int d=0){
cnt[l[u]][d]++;
vals[l[u]].pb(d);
for(int v:adj[u]) dfs0(v,d+1);
}
map<int, int> count_by_color[N];
deque<int> count_by_depth[N];
const int LIMIT=150;
int res_by_color[N][LIMIT];
ii ans={0,0};
int n,k;
void dfs(int u, int d=0){
count_by_color[u][l[u]]++;
count_by_depth[u]={1};
forn(c,LIMIT) res_by_color[u][c]=min(1,cnt[c][d]);
for(int v:adj[u]){
dfs(v,d+1);
if(sz(count_by_color[v])>sz(count_by_color[u])) swap(count_by_color[u],count_by_color[v]);
for(auto&[key,value]:count_by_color[v]) count_by_color[u][key]+=value;
count_by_depth[v].emplace_front(0);
if(sz(count_by_depth[v])>sz(count_by_depth[u])) swap(count_by_depth[u],count_by_depth[v]);
forn(c,LIMIT) res_by_color[u][c]+=res_by_color[v][c];
forn(h,sz(count_by_depth[v])){
forn(c,LIMIT){
res_by_color[u][c]-=min(count_by_depth[u][h],cnt[c][h+d])+min(count_by_depth[v][h],cnt[c][h+d]);
}
count_by_depth[u][h]+=count_by_depth[v][h];
forn(c,LIMIT){
res_by_color[u][c]+=min(count_by_depth[u][h],cnt[c][h+d]);
}
}
}
int res=l[u]<=LIMIT?res_by_color[u][l[u]]:0;
if(l[u]>LIMIT) for(int h:vals[l[u]]){
if(h<d) continue;
if(h-d>sz(count_by_depth[u])) break;
res+=min(count_by_depth[u][h-d],cnt[l[u]][h]);
}
int cost=res-count_by_color[u][l[u]];
ans=max(ans,ii{res,-cost});
}
int main(){
ios::sync_with_stdio(0);
cin.tie(0);
cin>>n>>k;
forn(i,n) cin>>l[i];
bool flag=true;
forsn(i,1,n){
int b; cin>>b;
adj[b].pb(i);
if(b!=i-1) flag=false;
}
vi q(k,0);
int res=0;
dforn(i,n){
res=max(res,++q[l[i]]);
}
if(flag){
cout<<res<<' '<<0<<'\n';
return 0;
}
vi colors(k);
iota(all(colors),0);
sort(all(colors),[&](const int &lhs, const int &rhs){
return q[lhs]>q[rhs];
});
vi pos_by_color(k);
forn(i,k) pos_by_color[colors[i]]=i;
forn(i,n) l[i]=pos_by_color[l[i]];
dfs0(0);
forn(i,k){
sort(all(vals[i]));
vals[i].erase(unique(all(vals[i])),end(vals[i]));
}
dfs(0);
cout<<ans.fst<<' '<<-ans.snd<<'\n';
return 0;
}
