#include <bits/stdc++.h>
using namespace std;
#define int long long
#define rep(i,a,b) for (int i = a; i <= b; i++)
#define per(i,a,b) for (int i = a; i >= b; i--)
#define pii pair<int,int>
#define pb push_back
#define fi first
#define se second
#define all(v) (v).begin(), (v).end()
#define endl '\n'
const int MAXN = 1e5+10;
const int INF = 1e18+10;
const int MOD = 1e9+7;
vector<int> g[MAXN];
int a[MAXN], par[MAXN], dep[MAXN], tin[MAXN],tout[MAXN], t=0;
int cnt[MAXN], amt[MAXN], dp[MAXN], chd[MAXN]; // ccol<=B
const int B = 360;
vector<int> invcol[MAXN];
vector<pii> lvl[MAXN];
void dfs(int u, int p = -1) {
tin[u] = ++t;
lvl[dep[u]].pb({tin[u], lvl[dep[u]].size()+1});
for(int &v : g[u]) if(v!=p) {
dep[v] = dep[u]+1;
dfs(v,u);
dp[u] = max(dp[u],dp[v] + 1);
}
tout[u] = ++t;
}
bool isch(int u, int v) {
// is u ch v
return tin[u] >= tin[v] && tout[u] <= tout[v];
}
vector<pii> imp;
void fimp(int u, int col = -1, int p = -1) {
if(a[u] == col) {
imp.pb({tin[u],u});
col = -1;
}
for(int &v : g[u]) if(v!=p) {
fimp(v,col,u);
}
}
void solve() {
int n,k; cin >> n >> k;
rep(i,1,n) {
cin >> a[i];
a[i]++;
invcol[a[i]].pb(i);
}
rep(i,2,n) {
cin >> par[i];
par[i]++;
g[par[i]].pb(i);
}
dfs(1);
rep(i,0,n) lvl[i].pb({INF,(int)lvl[i].size()+1});
pii ans = {1,0};
rep(cl,1,k) {
if(invcol[cl].size() <= B) continue;
imp.clear();
fimp(1,cl);
for(int &u : invcol[cl]) {
chd[u] = 0;
}
rep(i,0,n) {
cnt[i] = 0;
}
for(int &u : invcol[cl]) {
cnt[dep[u]]++;
}
for(int &u : invcol[cl]) {
auto it = upper_bound(all(imp), (pii){tin[u],INF});
if(it==imp.begin()) continue;
it--;
if(tout[it->se] >= tout[u]) chd[it->se]++;
}
for(auto &[_,u] : imp) {
int cans = 0, cch = 0;
rep(d,dep[u],dep[u]+dp[u]) {
amt[d] = upper_bound(all(lvl[d]), (pii){tout[u],INF})->se - lower_bound(all(lvl[d]),(pii){tin[u],0})->se;
//cout << u << ' ' <<d << ' '<< amt[d] << ' ' <<cnt[d] << endl;
cans += min(amt[d],cnt[d]);
cch += min(amt[d],cnt[d]);
}
cch -= chd[u];
ans = max(ans, {cans,-cch});
}
}
rep(cl,1,k) {
if(invcol[cl].size() > B) continue;
vector<pii> ipdep;
for(int &u : invcol[cl]) {
ipdep.pb({dep[u],0});
}
sort(all(ipdep));
ipdep.erase(unique(all(ipdep)),ipdep.end());
for(int &u : invcol[cl]) cnt[dep[u]]++;
for(int &u : invcol[cl]) {
int cans = 0, cch = 0;
for(auto &[d,amtt] : ipdep) {
if(d <= dep[u]) continue;
amt[d] = upper_bound(all(lvl[d]), (pii){tout[u],0})->se - lower_bound(all(lvl[d]),(pii){tin[u],0})->se;
}
for(int &v : invcol[cl]) {
if(isch(v,u)) {
cans++;
amt[dep[v]]--;
}
}
for(int &v : invcol[cl]) {
if(!isch(v,u) && dep[v]>dep[u] && amt[dep[v]]) {
cans++;
cch++;
amt[dep[v]]--;
}
}
ans = max(ans,{cans,-cch});
}
}
cout << ans.fi << ' ' << -ans.se << endl;
}
int32_t main() {
ios_base::sync_with_stdio(0); cin.tie(nullptr);
int tt = 1;
//cin >> tt;
while (tt--) solve();
return 0;
}
