#include<bits/stdc++.h>
using namespace std;
const int maxn = 1e5 + 5;
using ll = long long;
vector<int> adj[maxn], dis(maxn, 1e6), a(maxn), c(maxn), b(maxn), in(maxn), out(maxn), lvl[maxn];
int H = 0;
int timer = -1;
void euler(int u) {
timer++;
in[u] = timer;
a[timer] = u;
lvl[dis[u]].push_back(in[u]);
for(int v : adj[u]) {
dis[v] = dis[u] + 1;
H = max(H, dis[v]);
euler(v);
}
out[u] = timer;
}
int main() {
ios::sync_with_stdio(0);
cin.tie(0);
int n, k;
cin >> n >> k;
bool w = 1;
for(int i = 0; i < n; i++) {
cin >> c[i];
}
for(int i = 1; i < n; i++) {
cin >> b[i];
adj[b[i]].push_back(i);
if(b[i] != i - 1) w = 0;
}
if(w) {
int mx = 0;
int cnt[k + 1] {};
for(int i = n - 1; i >= 0; i--) {
cnt[c[i]]++;
mx = max(mx, cnt[c[i]]);
}
cout << mx << ' ' << 0 << '\n';
} else {
dis[0] = 0;
lvl[0].push_back(0);
euler(0);
vector<int> cnt[H + 1][k + 1];
for(int i = 1; i <= H; i++) {
for(int x : lvl[i]) {
cnt[i][c[a[x]]].push_back(x);
}
}
int mx = 1, sw = 0;
for(int i = 0; i < n; i++) {
int l = dis[i];
int mxx = 1, swp = 0;
for(int j = l + 1; j <= H; j++) {
int x = lower_bound(lvl[j].begin(), lvl[j].end(), in[i]) - lvl[j].begin();
int y = upper_bound(lvl[j].begin(), lvl[j].end(), out[i]) - lvl[j].begin() - 1;
int mn = min((int)cnt[j][c[i]].size(), y - x + 1);
x = lower_bound(cnt[j][c[i]].begin(), cnt[j][c[i]].end(), in[i]) - cnt[j][c[i]].begin();
y = upper_bound(cnt[j][c[i]].begin(), cnt[j][c[i]].end(), out[i]) - cnt[j][c[i]].begin() - 1;
mxx += mn;
swp += (mn - (y - x + 1));
}
if(mxx > mx) {
mx = mxx;
sw = swp;
} else if(mxx == mx) sw = min(sw, swp);
}
cout << mx << ' ' << sw << '\n';
}
return 0;
}
