#include<bits/stdc++.h>
using namespace std;
#define IOS cin.tie(nullptr)->sync_with_stdio(0),cin.exceptions(cin.failbit);
#define lb(x) (x)&-(x)
#define all(x) (x).begin(),(x).end()
#define ll long long
constexpr int maxN=1e5+5,blk = 500;
int n,k,col[maxN],in[maxN],out[maxN],cnt,dep[maxN];
vector<int> adj[maxN];
vector<tuple<int,int,int>> ask[maxN];
vector<int> grp[maxN];
int nowcol,rec[maxN];
bitset<maxN> vis;
int mx,mnopr;
inline void dfs(int now){
in[now] = ++cnt;
for(int i:adj[now]){
dep[i] = dep[now]+1;
dfs(i);
}
out[now] = cnt+1;
}
inline deque<int> dfs2(int now){
deque<int> ret;
ret.emplace_back(1);
for(int i:adj[now]){
auto tmp = dfs2(i);
tmp.emplace_front(0);
if(tmp.size()>ret.size())swap(tmp,ret);
for(int j = 0;j<tmp.size();j++)
ret[j] = ret[j]+tmp[j];
}
int res = 0,opr = 0;
for(auto [i,v,x]:ask[now]){
int add = min(ret[i],v);
opr+=add-x;
res+=add;
}
if(mx<res)mx = res,mnopr = opr;
else if(mx==res&&mnopr>opr)mnopr = opr;
return ret;
}
inline deque<pair<int,int>> dfs3(int now){
deque<pair<int,int>> ret;
ret.emplace_back(1,col[now]==nowcol);
vis[now] = 1;
for(int i:adj[now]){
auto tmp = dfs3(i);
tmp.emplace_front(0,0);
if(tmp.size()>ret.size())swap(tmp,ret);
for(int j = 0;j<tmp.size();j++)
ret[j] = {ret[j].first+tmp[j].first,ret[j].second+tmp[j].second};
}
return ret;
}
int main(){
IOS
cin>>n>>k;
for(int i = 0;i<n;i++)cin>>col[i],grp[col[i]].emplace_back(i);
for(int i = 1;i<n;i++){
int p;cin>>p;
adj[p].emplace_back(i);
}
dfs(0);
for(int i = 0;i<k;i++){
sort(all(grp[i]),[&](int a,int b){return dep[a]<dep[b];});
int sz = grp[i].size();
if(sz>blk){
fill(rec,rec+n+1,0);
vis.reset();
for(int j:grp[i])rec[col[j]]++;
for(int j:grp[i])if(!vis[j]){
nowcol = i;
auto it = dfs3(j);
int res = 0,opr = 0;
for(int i = dep[j],j = 0;j<it.size();i++,j++){
int add = min(it[j].first,rec[i]);
opr+=add-it[j].second;
res+=add;
}
if(res>mx)mx = res,mnopr = opr;
else if(mx==res&&mnopr>opr)mnopr = opr;
}
}
else {
for(int j = 0;j<sz;j++){
int v = grp[i][j];
for(int k = 0,num = 0,num2 = 0;k<sz;k++){
int u = grp[i][k];
if(dep[u]>=dep[v]){
num++;
if(in[u]>=in[v]&&out[u]<=out[v])num2++;
if(k==sz-1||dep[grp[i][k]]<dep[grp[i][k+1]])
ask[v].emplace_back(dep[u]-dep[v],num,num2),num = 0,num2 = 0;
}
}
}
}
}
dfs2(0);
cout<<mx<<' '<<mnopr<<'\n';
}
