#include<bits/stdc++.h>
using namespace std ;
#define F first
#define S second
const int N = 1e5+5 ;
int n , k , color[N] , par[N] , deep[N] , in[N] , out[N] , t ;
vector<int> child[N] , cpos[N] , dcnt[N] , cd[N] ;
pair<int,int> ans ;
void dfs(int node){
in[node]=++t ;
dcnt[deep[node]].push_back(in[node]) ;
cd[color[node]].push_back(deep[node]) ;
for(int i:child[node]) deep[i]=deep[node]+1 , dfs(i) ;
out[node]=++t ;
}
void dfs1(int node , int c){
if(color[node]==c){
vector<int> v , v1 ;
queue<pair<int,int>> q ;
q.push({node,0}) ;
int temp = 0 , change = 0 ;
while(!q.empty()){
int x = q.front().F , d = q.front().S ; q.pop() ;
if(v.size()<=d) v.push_back(0) , v1.push_back(0) ;
if(color[x]==color[node]) temp++ , v1[d]++ ;
else v[d]++ ;
for(int i:child[x]) q.push({i,d+1}) ;
}
for(int i=0 ; i<v.size() ; i++){
int cur = upper_bound(cd[color[node]].begin(),cd[color[node]].end(),deep[node]+i)-lower_bound(cd[color[node]].begin(),cd[color[node]].end(),deep[node]+i) ;
temp+=min(v[i],cur-v1[i]) ; change+=min(v[i],cur-v1[i]) ;
}
ans = max(ans,{temp,-change}) ;
return ;
}
for(int i:child[node]) dfs1(i,c) ;
}
int main(){
ios::sync_with_stdio(0),cin.tie(0),cout.tie(0) ;
cin >> n >> k ; par[0] = -1 ;
for(int i=0 ; i<n ; i++) cin >> color[i] , cpos[color[i]].push_back(i) ;
for(int i=1 ; i<n ; i++) cin >> par[i] , child[par[i]].push_back(i) ;
dfs(0) ;
for(int i=0 ; i<k ; i++){
sort(cd[i].begin(),cd[i].end()) ;
dfs1(0,i) ;
}
cout << ans.F << ' ' << -ans.S << '\n' ;
return 0 ;
}
