#include<bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
using namespace std;
typedef long long int ll;
typedef vector<ll> vi;
typedef vector<vector<ll>> vvi;
typedef pair<ll,ll> pi;
typedef map<ll,ll> mi;
#define ff first
#define ss second
#define srt(a) sort(a.begin(),a.end());
#define fip(k, n) for (ll i = k; i < n; i++)
#define fjp(k, n) for (ll j = k; j < n; j++)
#define fin(k, n) for (ll i = k; i >= n; i--)
#define fjn(k, n) for (ll j = k; j >= n; j--)
#define fp(k, n, m) for (ll k = n; k < m; k++)
#define fn(k, n, m) for (ll k = n; k >= m; k--)
#define ordered_set tree<pi, null_type,less< pi >, rb_tree_tag,tree_order_statistics_node_update>
#define totalOne(n) __builtin_popcount(n)
#define backZero(n) __builtin_ctzll(n)
#define frontZero(n) __builtin_clzll(n)
#define fx(k) for ( auto x : k )
#define test ll t;cin >> t;while (t--)
#define nli "\n"
// ==========================(debug)============================================================================================== //
#ifdef SAMI
#define debug(x) cerr<<#x;cerr<<" ";_printn(x);cerr<<nli;
#define debg() cerr<<nli;
#else
#define debug(x)
#define debg()
#endif
void _printn(ll x){ cerr<<x<<" "; }
void _printn(int x){ cerr<<x<<" "; }
void _printn(double x){ cerr<<x<<" "; }
void _printn(string x){ cerr<<x<<" "; }
void _printn(char x){ cerr<<x<<" "; }
void _printn(bool x){ cerr<<x<<" "; }
template<class T,class V>void _printn(pair<T,V> vv);
template<class T> void _printn(vector<T> vv);
template<class T> void _printn(set<T> vv);
template<class T,class V> void _printn(map<T,V> vv);
template<class T> void _printn(multiset<T> vv);
template<class T,class V>void _printn(pair<T,V> vv){ cerr<<"( ";_printn(vv.ff);cerr<<",";_printn(vv.ss);cerr<<")";}
template<class T> void _printn(vector<T> vv){ cerr<<"[ "; for(auto xx:vv){ _printn(xx);cerr<<" "; } cerr<<"]"; };
template<class T> void _printn(set<T> vv){ cerr<<"{ "; for(auto xx:vv){ _printn(xx);cerr<<" "; } cerr<<"}"; };
template<class T> void _printn(multiset<T> vv){ cerr<<"{ "; for(auto xx:vv){ _printn(xx);cerr<<" "; } cerr<<"}"; };
template<class T,class V> void _printn(map<T,V> vv){ cerr<<"{ "; for(auto xx:vv){ _printn(xx);cerr<<" "; } cerr<<"}"; };
// ==========================(debug)============================================================================================== //
ll n,m,tp,tp2,res,cnt,sum,tptp,ans;
const ll mx = 5e5+5;
const ll mod = 1e9+7;
// ==========================(MOD)=============================================================================================== //
ll mod_add(ll aa,ll bb){ return ((aa%mod)+(bb%mod))%mod; }
ll mod_minus(ll aa,ll bb){ return (((aa%mod)-(bb%mod))+10*mod)%mod; }
ll mod_mul(ll aa,ll bb){ return ((aa%mod)*(bb%mod))%mod; }
ll mod_power(ll aa,ll bb){ aa%=mod; ll empowered = 1; bb%=mod-1; while(bb > 0){ if(bb & 1) empowered = mod_mul(empowered,aa); bb = bb >> 1; aa = mod_mul(aa,aa); } return empowered; }
ll mod_divi(ll aa,ll bb){ aa=mod_mul(aa,mod_power(bb,mod-2)); return aa; }
// ==========================(MOD)=============================================================================================== //
bool f = false;
ll a[mx];
vi adj[mx];
ll tnc[mx];
ll dp[mx];
ll dp2[mx];
ll dep[mx];
ll st[mx];
ll en[mx];
pi nas;
vi pd[mx];
vi lss[mx];
ll timer = 0;
ll l,r,mid,l1,r1,mid1,pt,pt2;
bool mark[mx];
ll get(ll idx,ll k){
l = 0;
r = pd[k].size()-1;
pt = pd[k].size();
while(l<=r){
mid = l + (r-l)/2;
if(pd[k][mid]>=st[idx]){
pt = mid;
r = mid - 1;
}else
l = mid + 1;
}
l1 = 0;
r1 = pd[k].size()-1;
pt2 = -1;
while(l1<=r1){
mid1 = l1 + (r1-l1)/2;
if(pd[k][mid1]<=en[idx]){
pt2 = mid1;
l1 = mid1 + 1;
}else
r1 = mid1 - 1;
}
return max(0ll,pt2-pt+1);
}
void dfs(ll u){
st[u] = timer;
timer++;
fx(adj[u]){
dep[x] = dep[u] + 1;
dfs(x);
}
en[u] = timer-1;
return;
}
int main(){
ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
#ifdef SAMI
freopen("input1.txt", "r", stdin);
freopen("output1.txt", "w", stdout);
freopen("error1.txt", "w", stderr);
#endif // ONLINE_JUDGE
cin>>n>>m;
fip(0,n){
cin>>a[i];
lss[a[i]].push_back(i);
}
ll sr;
fip(1,n){
cin>>sr;
adj[sr].push_back(i);
}
nas = {-1e18,-1e18};
dep[0] = 0;
dfs(0);
fip(0,n)
pd[dep[i]].push_back(st[i]);
fip(0,n){
srt(pd[i]);
}
fp(kk,0,m){
fjp(0,lss[kk].size()){
tp = lss[kk][j];
dp2[dep[tp]]++;
}
fip(0,lss[kk].size()){
ans = 0;
res = 0;
fjp(0,lss[kk].size()){
tp = lss[kk][i];
tp2 = lss[kk][j];
tnc[dep[tp2]] = get(tp,dep[tp2]);
if(st[tp]<=st[tp2] && en[tp]>=en[tp2])
dp[dep[tp2]]++;
}
fjp(0,lss[kk].size()){
tp2 = lss[kk][j];
if(!mark[dep[tp2]]){
mark[dep[tp2]] = 1;
ans += min(tnc[dep[tp2]],dp2[dep[tp2]]);
res += min(tnc[dep[tp2]],dp2[dep[tp2]]) - dp[dep[tp2]];
}
}
fjp(0,lss[kk].size()){
tp2 = lss[kk][j];
mark[dep[tp2]] = 0;
}
fjp(0,lss[kk].size()){
tp = lss[kk][i];
tp2 = lss[kk][j];
tnc[dep[tp2]] = 0;
if(st[tp]<=st[tp2] && en[tp]>=en[tp2])
dp[dep[tp2]]--;
}
nas = max(nas,{ans,-res});
}
fjp(0,lss[kk].size()){
tp = lss[kk][j];
dp2[dep[tp]]--;
}
}
cout<<nas.ff<<" "<<(-nas.ss)<<nli;
cerr << "Time elapsed: " << setprecision(6) << 1000.0 * clock() / CLOCKS_PER_SEC << "ms\n";
return 0;
}
