#include <bits/stdc++.h>
#define int long long
#define sz(a) (int)a.size()
#define all(a) a.begin(), a.end()
using namespace std;
vector<vector<int>> child;
vector<int> depthCOUNT;
vector<int> depth;
vector<vector<int>> parent;
int totMX=0;
int totSWITCH=0;
int SQRT;
vector<int> l;
int need;
const int LOG=31;
int lca(int a, int b){
if(depth[a]>depth[b]) swap(a,b);
int d=depth[b]-depth[a];
for (int i = LOG-1; i >= 0; i--)
{
if(d&(1<<i)) b=parent[b][i];
}
if(a==b) return a;
for (int i = LOG-1; i >= 0; i--){
if(parent[a][i]!=parent[b][i]){
a=parent[a][i];
b=parent[b][i];
}
}
return parent[a][0];
}
vector<int> depthHAS;
vector<int> depthNOTHAS;
vector<int> depthNEDED;
vector<vector<int>> lang;
int N;
int addALLCHILD(int x){
if(l[x]==need) depthHAS[depth[x]]++;
else depthNOTHAS[depth[x]]++;
int sm=depth[x];
for (auto u : child[x])
{
sm=max(sm,addALLCHILD(u));
}
return sm;
}
void dfs(int x){
if(l[x]==need){
int mx=addALLCHILD(x);
int sm=1;
int swtch=0;
for (int j = depth[x]+1; j <= mx;j++)
{
int gave=min(depthNEDED[j]-depthHAS[j],depthNOTHAS[j]);
sm+=depthHAS[j]+gave;
swtch+=gave;
}
for (int j = depth[x]; j <= mx;j++)
{
depthHAS[j]=0;
depthNOTHAS[j]=0;
}
if(sm>totMX){
totMX=sm;
totSWITCH=swtch;
}else if(sm==totMX){
totSWITCH=min(totSWITCH,swtch);
}
return;
}else{
for (auto u : child[x])
{
dfs(u);
}
return;
}
}
unordered_map<int,int> dfs2(int x){
vector<unordered_map<int,int>> mps;
for (auto u : child[x])
{
mps.push_back(dfs2(u));
}
mps.push_back({});
mps[sz(mps)-1][depth[x]]++;
sort(all(mps), [&](auto &aa, auto &bb) {return sz(aa)>sz(bb);});
for (int i = 1; i < sz(mps); i++)
{
for (auto u : mps[i])
{
mps[0][u.first]+=u.second;
}
}
unordered_map<int,pair<int,int>> dpth;
if(sz(lang[l[x]])<SQRT){
for (int i = 0; i < sz(lang[l[x]]); i++)
{
if(lang[l[x]][i]==x||depth[lang[l[x]][i]]<=depth[x]) continue;
if(lca(lang[l[x]][i],x)==x){
dpth[depth[lang[l[x]][i]]].first++;
}else{
dpth[depth[lang[l[x]][i]]].second++;
}
}
int sm=1;
int swtch=0;
for (auto u : dpth)
{
int gave=min(u.second.second,mps[0][u.first]-u.second.first);
sm+=u.second.first+gave;
swtch+=gave;
}
if(sm>totMX){
totMX=sm;
totSWITCH=swtch;
}else if(sm==totMX){
totSWITCH=min(totSWITCH,swtch);
}
}
return move(mps[0]);
}
signed main() {
ios_base::sync_with_stdio(false); cin.tie(nullptr);
int K; cin >> N >> K;
l.resize(N);
parent.resize(N,vector<int>(LOG,0));
depth.resize(N);
child.resize(N);
lang.resize(K);
depthHAS.resize(N,0);
depthNOTHAS.resize(N,0);
SQRT=sqrt(N);
unordered_map<int,int> cnt;
for (int i = 0; i < N; i++) cin >> l[i];
for (int i = 0; i < N; i++) cnt[l[i]]++;
for (int i = 0; i < N; i++) lang[l[i]].push_back(i);
int mx=cnt[l[0]];
need=1-l[0];
parent[0][0]=0;
for (int i = 1; i < N; i++) {
cin >> parent[i][0];
child[parent[i][0]].push_back(i);
}
for (int j = 1; j < LOG; j++)
{
for (int i = 0; i < N; i++)
{
parent[i][j]=parent[parent[i][j-1]][j-1];
}
}
depthNEDED.resize(N,0);
queue<int> que;
que.push(0);
while(!que.empty()){
int x=que.front(); que.pop();
for (auto u : child[x])
{
depth[u]=depth[x]+1;
que.push(u);
}
}
dfs2(0);
for (int i = 0; i < K; i++)
{
if(sz(lang[i])>=SQRT){
for (int j = 0; j < sz(lang[i]); j++) depthNEDED[depth[lang[i][j]]]++;
need=i;
dfs(0);
for (int j = 0; j < sz(lang[i]); j++) depthNEDED[depth[lang[i][j]]]=0;;
}
}
if(mx>=totMX){
totMX=mx;
totSWITCH=0;
}
cout << totMX << " " << totSWITCH << "\n";
return 0;
}
