#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define fi first
#define se second
#define pb push_back
#define sz(a) (ll) a.size()
#define all(x) (x).begin(), (x).end()
#define rep(i, a, b) for(int i=a; i<b; i++)
#define rrep(i, a, b) for(ll i=a; i>=b; i--)
#define vl vector<ll>
#define vpll vector<pair<ll, ll>>
#define vvl vector<vector<ll>>
#define pll pair<ll, ll>
int n, k, mxlvl, timer;
pair<int, int> ans;
vector<int> lvl, pa, colour, pl, sz, pltoid;
vector<vector<int>> flr, cld;
void assign_lvl(int id){
mxlvl=max(mxlvl, lvl[id]);
pl[id]=timer;
pltoid[timer]=id;
timer++;
sz[id]=1;
for(auto& u : cld[id]){
lvl[u]=lvl[id]+1;
assign_lvl(u);
sz[id]+=sz[u];
}
}
void find(int id){
int currpl=pl[id];
vector<int> canfill(mxlvl, 0), have(mxlvl, 0);
for(int i=0; i<sz[id]; i++){
int currid=pltoid[currpl];
canfill[lvl[currid]]++;
if(colour[currid]==colour[id]) have[lvl[currid]]++;
currpl++;
}
pair<int, int> currans={0, 0};
for(int i=0; i<mxlvl; i++){
if(canfill[i]==0) continue;
currans.fi+=min(canfill[i], flr[i][colour[id]]);
if(canfill[i]>have[i] && flr[i][colour[id]]>have[i]){
currans.se+=min(canfill[i], flr[i][colour[id]])-have[i];
}
}
if(currans.fi>ans.fi) ans=currans;
else if(currans.fi==ans.fi) ans.se=min(ans.se, currans.se);
}
void gocolour(int color){
for(int i=0; i<n; i++){
int id=pltoid[i];
if(colour[id]==color){
find(id);
i+=sz[id]-1;
}
}
}
void f() {
cin >> n >> k;
mxlvl=0;
timer=0;
ans={-1, -1};
lvl.assign(n, 0);
pa.assign(n, 0); for(int i=0; i<n; i++) pa[i]=i;
colour.assign(n, 0);
pl.assign(n, 0);
sz.assign(n, 0);
pltoid.assign(n, 0);
flr.assign(0, vector<int>(0));
cld.assign(n, vector<int>(0));
for(int i=0; i<n; i++) cin >> colour[i];
for(int i=1; i<n; i++){
cin >> pa[i];
cld[pa[i]].pb(i);
}
assign_lvl(0);
mxlvl++;
flr.assign(mxlvl, vector<int>(k, 0));
for(int i=0; i<n; i++){
flr[lvl[i]][colour[i]]++;
}
for(int i=0; i<k; i++){
gocolour(i);
}
cout << ans.fi << ' ' << ans.se;
}
int main() {
int tc = 1;
// cin >> tc;
for (int i = 1; i <= tc; i++) {
// cout << endl << '#' << i << endl;
f();
cout << endl;
}
}
