#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(ll 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>
ll n, k, mxlvl, place;
pll tans;
vl l, pa, sz, lvl, pl;
vvl child;
/**cnt[level][colour][?]=pre*/
vector<vvl> cnt;
ll count(ll id, ll level, ll colour){
ll ret=cnt[level][colour][pl[id]+sz[id]-1];
if(pl[id]>0) ret-=cnt[level][colour][pl[id]-1];
return ret;
}
void ifme(ll id){
pll ans={0, 0};
rep(level, lvl[id]+1, mxlvl+1){
ll canfill=count(id, level, k), haveinside=count(id, level, l[id]), thislevel=cnt[level][l[id]][n-1];
canfill=min(canfill, thislevel);
ans.fi+=canfill;
ans.se+=canfill-haveinside;
}
ans.fi++;
if(tans.fi==-1) tans=ans;
if(tans.fi<ans.fi){
tans=ans;
} else if(tans.fi==ans.fi){
tans.se=min(tans.se, ans.se);
}
}
void prerun(ll x){
pl[x]=place;
place++;
mxlvl=max(mxlvl, lvl[x]);
for(auto& u : child[x]){
lvl[u]=lvl[x]+1;
prerun(u);
sz[x]+=sz[u];
}
}
void f() {
cin >> n >> k;
mxlvl=0;
place=0;
tans={-1, -1};
l.resize(n);
pa.resize(n);
sz.assign(n, 1);
lvl.assign(n, 0);
pl.assign(n, 0);
child.assign(n, vl(0));
cnt={};
for(auto& u : l) cin >> u;
rep(i, 1, n){
ll x; cin >> x;
pa[i]=x;
child[x].pb(i);
}
lvl[0]=0;
prerun(0);
cnt.assign(mxlvl+1, vvl(k+1, vl(n, 0)));
//cnt[level][l][?]=pre
rep(i, 0, n){
cnt[lvl[i]][l[i]][pl[i]]++;
cnt[lvl[i]][k][pl[i]]++;
}
rep(level, 0, mxlvl+1){
rep(colour, 0, k+1){
rep(i, 1, n) cnt[level][colour][i]+=cnt[level][colour][i-1];
}
}
rep(i, 0, n){
ifme(i);
}
cout << tans.fi << ' ' << tans.se;
}
int main() {
int tc = 1;
// cin >> tc;
for (int i = 1; i <= tc; i++) {
// cout << '#' << i << endl;
f();
cout << endl;
}
}
