#include <bits/stdc++.h>
using namespace std;
#define rng(i,a,b) for(int i=int(a);i<=int(b);i++)
#define rep(i,b) rng(i,0,b-1)
#define gnr(i,b,a) for(int i=int(b);i>=int(a);i--)
#define per(i,b) gnr(i,b-1,0)
#define pb push_back
#define eb emplace_back
#define fi first
#define se second
#define bg begin()
#define ed end()
#define all(x) x.bg,x.ed
#define si(x) int(x.size())
template<class t> using vc=vector<t>;
template<class t> using vvc=vc<vc<t>>;
typedef long long ll;
using pii=pair<int,int>;
using vi=vc<int>;
using uint=unsigned;
using ull=unsigned long long;
using pil=pair<int,ll>;
using pli=pair<ll,int>;
using pll=pair<ll,ll>;
using t3=tuple<int,int,int>;
#define N_ 110000
vi E[N_], G[N_];
int n, K;
const int BL = 200;
int w[N_], Dep[N_], Num[N_], cnt, Ed[N_], Rev[N_];
int Left[N_], Right[N_], Ans, Ans2, T1[N_], T2[N_];
map<int,int>C[N_];
void DFS(int a){
Num[a] = ++cnt;
for(auto &x:E[a]){
Dep[x]=Dep[a]+1;
DFS(x);
}
Ed[a] = ++cnt;
}
void Do1(int a){
int pv = -1, Mx = -1;
for(auto &x:E[a]){
Do1(x);
if(Mx < si(C[x])){
pv = x;
Mx = si(C[x]);
}
}
if(pv!=-1){
swap(C[a],C[pv]);
}
C[a][Dep[a]]+=1;
for(auto &x:E[a]){
if(x==pv)continue;
for(auto &[d,c] : C[x]) C[a][d] += c;
}
if(si(G[w[a]]) < BL){
for(auto &t: G[w[a]]){
T1[Dep[t]]++;
if(Num[a] <= Num[t] && Num[t] <= Ed[a]){
T2[Dep[t]]++;
}
}
int s = 0, s2 = 0;
for(auto &t: G[w[a]]){
int d = Dep[t];
if(!T1[d])continue;
int c = C[a][d];
s += min(T1[d], c);
s2 += min(T2[d],c);
T1[d]=T2[d]=0;
}
if(Ans < s || (Ans==s && Ans2 > s-s2)){
Ans = s;
Ans2 = s-s2;
}
}
}
int DMX, CC[N_], s2;
void Go(int a, int col){
int d = Dep[a];
CC[d]++;
DMX = max(DMX, d);
if(w[a]==col)s2++;
for(auto &x: E[a]){
Go(x,col);
}
}
void Do2(int a, int col){
if(w[a]==col){
DMX = Dep[a];
s2=0;
Go(a, col);
int s=0;
rng(i,Dep[a],DMX){
s += min(CC[i],T1[i]);
CC[i]=0;
}
if(Ans < s || (Ans==s && Ans2 > s-s2)){
Ans = s;
Ans2 = s-s2;
}
return;
}
for(auto &x : E[a]){
Do2(x, col);
}
}
int main(){
scanf("%d%d",&n,&K);
rep(i,n){
scanf("%d",&w[i]);
G[w[i]].pb(i);
}
rng(i,1,n-1){
int a;
scanf("%d",&a);
E[a].pb(i);
}
DFS(0);
Do1(0);
rep(i,K){
if(si(G[i]) >= BL){
for(auto &u: G[i])T1[Dep[u]]++;
Do2(0,i);
for(auto &u: G[i])T1[Dep[u]]--;
}
}
printf("%d %d\n",Ans,Ans2);
}
