#include<bits/stdc++.h>
using namespace std;
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
#define ll long long
#define double long double
#define ordered_set tree<int, null_type,less<int>, rb_tree_tag,tree_order_statistics_node_update>
#define S second
#define F first
#define fall(i,a,n) for(int i=a;i<=n;i++)
#define rfall(i,a,n) for(int i=a;i>=n;i--)
#define pb push_back
#define all(x) x.begin(),x.end()
#define lsb(x) (x & -x)
#define sz(x) (int)x.size()
const int MAXN=2e5+10;
const int MAXL=22;
const int inf=1e18;
const int MOD=998244353;
const int HASHMOD=1000000001237;
const int HASHBASE=146527;
typedef pair<int,int> pii;
typedef tuple<int,int,int> trio;
typedef tuple<int,int,int,int> squad;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
//auto start=chrono::high_resolution_clock::now();
/*auto end=chrono::high_resolution_clock::now();
auto dur=chrono::duration<double>(end-start).count();
cout<<dur<<"\n";*/
map<int,map<int,int>> mp[MAXN]; //vertice,cor,dep
map<int,int> alltree[MAXN],tot[MAXN];
int n,k,cor[MAXN],raiz,f[MAXN],dep[MAXN],tin[MAXN],cur,dp[MAXN],ans,swa,cure,curs,op;
vector<int> g[MAXN],caras[MAXN];
vector<pii> v[MAXN],td;
vector<bool> init;
void dfs(int x){
f[cor[x]]++;
alltree[cor[x]][dep[x]]++;
mp[x][cor[x]][dep[x]]++;
v[x].pb({cor[x],dep[x]});
tot[x][dep[x]]++;
for(auto u:g[x]){
dfs(u);
if(sz(v[u])>sz(v[x])) mp[x].swap(mp[u]),tot[x].swap(tot[u]),v[x].swap(v[u]);
for(auto [b,c]:v[u]){
mp[x][b][c]++;
v[x].pb({b,c});
tot[x][c]++;
}
}
f[cor[x]]--;
if(sz(caras[cor[x]])>raiz || f[cor[x]]) return;
int rs=0,sp=0;
vector<int> ad;
op+=sz(caras[cor[x]]);
for(auto u:caras[cor[x]]){
if(tin[u]>=tin[x] && tin[x]+dp[x]>=tin[u]){
rs++;
continue;
}
int q=tot[x][dep[u]]-mp[x][cor[x]][dep[u]];
if(q>0){
tot[x][dep[u]]--;
ad.pb(dep[u]);
rs++;
sp++;
}
}
for(auto u:ad) tot[x][u]++;
if(ans<rs || (ans==rs && sp<swa)) ans=rs,swa=sp;
}
void dfs1(int x){
tin[x]=++cur;
for(auto u:g[x]){
dep[u]=dep[x]+1;
dfs1(u);
dp[x]+=dp[u]+1;
}
}
void dfsset(int x){
td.pb({cor[x],dep[x]});
alltree[cor[x]][dep[x]]--;
for(auto u:g[x]) dfsset(u);
}
void dfstake(int x,int color){
if(cor[x]==color)cure++;
else if(alltree[color][dep[x]]) cure++,curs++,alltree[color][dep[x]]--,td.pb({color,dep[x]});
for(auto u:g[x]) dfstake(u,color);
}
void process(int x){
td.clear();
dfsset(x);
cure=curs=0;
dfstake(x,cor[x]);
if(ans<cure || (ans==cure && curs<swa)) ans=cure,swa=curs;
for(auto [u,j]:td) alltree[u][j]++;
}
void dfs2(int x){
f[cor[x]]++;
for(auto u:g[x]) dfs2(u);
f[cor[x]]--;
if(f[cor[x]] || sz(caras[cor[x]])<=raiz) return;
process(x);
}
int32_t main(){
std::ios_base::sync_with_stdio(false);
cin.tie(NULL);
cin>>n>>k;
raiz=sqrt(n);
fall(i,0,n-1){
cin>>cor[i];
caras[cor[i]].pb(i);
}
fall(i,1,n-1){
int p; cin>>p;
g[p].pb(i);
}
dfs1(0);
dfs(0);
fall(i,0,k-1) f[i]=0;
dfs2(0);
cout<<ans<<" "<<swa<<"\n";
}
