#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ordered_set tree<int, null_type,less<int>, rb_tree_tag,tree_order_statistics_node_update>
using namespace std;
using namespace __gnu_pbds;
#define g0(x) get<0>(x)
#define g1(x) get<1>(x)
#define g2(x) get<2>(x)
#define mt make_tuple
#define mp make_pair
#define pb push_back
#define int long long
#define f first
#define s second
#define pll pair<long long, long long>
#define iii tuple<int,int,int>
#define sz(x) (int)x.size()
#define all(x) x.begin(), x.end()
const int blk=305;
signed main(){
int n,k;cin>>n>>k;
vector<int> c(n); for(int i=0;i<n;i++)cin>>c[i];
vector<vector<int>> grp(n);
vector<int> pre(n, 0), post(n, 0), lay(n, 0);
vector<vector<int>> layer(n);
vector<vector<int>> ch(n);
for(int i=1;i<n;i++){
int b;cin>>b;
ch[b].pb(i);
}
int t=0;
auto dfs=[&](auto && dfs, int x) -> void{
pre[x]=t++;
layer[lay[x]].pb(pre[x]);
grp[c[x]].pb(x);
for(auto it: ch[x]){
lay[it]=lay[x]+1;
dfs(dfs, it);
}
post[x]=t-1;
};
dfs(dfs, 0);
pair<int,int> ans={0, 0};
for (int i=0;i<n;i++){
if(sz(grp[i]) < blk){
map<int,int> tot;
for(int j : grp[i]){
tot[lay[j]]++;
}
/*for (auto [l, totcnt] : tot){
printf("col %lld, layer %lld, cnt %lld\n", i, l, totcnt);
}*/
for(int j : grp[i]){
map<int,int> und;
for(int k : grp[i]){
if(pre[j] <= pre[k] and post[j] >= pre[k]){
und[lay[k]]++;
}
}
pll cand={0, 0};
for(auto [l, totcnt] : tot){
int undcnt=und[l];
int sl=upper_bound(all(layer[l]), post[j])-lower_bound(all(layer[l]), pre[j]);
//printf("parent %lld, l %lld, totcnt %lld, sl %lld\n", j, l, totcnt, sl);
int u=min(sl, totcnt);
int cost=u-und[l];
cand.f += u, cand.s += cost;
}
if(cand.f > ans.f or (cand.f == ans.f and cand.s < ans.s)) ans=cand;
}
}
else {
vector<int> stk, heads;
map<int,int> tot;
for(int j : grp[i]){
tot[lay[j]]++;
}
/*for (auto [l, totcnt] : tot){
printf("col %lld, layer %lld, cnt %lld\n", i, l, totcnt);
}*/
for(int j : grp[i]){
while(!stk.empty() and post[stk.back()] < pre[j]){
stk.pop_back();
}
if(stk.empty()){
heads.pb(j);
stk.pb(j);
}
}
for(int j : heads){
//printf("col %lld, head j %lld\n", i, j);
map<int, int> slays, und;
auto dfs2=[&](auto && dfs2, int x)->void{
slays[lay[x]]++;
if(c[x] == i) und[lay[x]]++;
for(auto it : ch[x]){
dfs2(dfs2, it);
}
};
dfs2(dfs2, j);
pll cand={0, 0};
for(auto [l, sl]: slays){
int undcnt=und[l];
int totcnt=tot[l];
int u=min(sl, totcnt);
int cost=u-und[l];
cand.f += u, cand.s += cost;
//printf("layer %lld, sl %lld, undcnt %lld, totcnt %lld, u %lld, cost %lld\n",
//l, sl, undcnt, totcnt, u, cost);
}
if(cand.f > ans.f or (cand.f == ans.f and cand.s < ans.s)) ans=cand;
}
}
}
cout<<ans.f<<" "<<ans.s;
}
