#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], nadj[maxn * 2 + 1], v[maxn];
vector<int> par(maxn, -1), vec;
int H = 0;
int timer = -1;
int n, k;
void euler(int u) {
timer++;
in[u] = timer;
a[timer] = u;
if(v[c[u]].empty()) {
nadj[n + c[u]].push_back(u);
par[u] = n + c[u];
} else {
nadj[v[c[u]].back()].push_back(u);
par[u] = v[c[u]].back();
}
v[c[u]].push_back(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);
}
v[c[u]].pop_back();
out[u] = timer;
}
void dfs(int u) {
for(int v : nadj[u]) {
vec.push_back(dis[v]);
dfs(v);
}
}
int main() {
ios::sync_with_stdio(0);
cin.tie(0);
cin >> n >> k;
bool w = 1;
int mx = 1, sw = 0;
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];
map<pair<int, int>, vector<int>> cnt;
for(int i = 1; i <= H; i++) {
for(int x : lvl[i]) {
cnt[{i, c[a[x]]}].push_back(x);
}
}
// for(int i = 0; i < n + k; i++) {
// cout << i << " : ";
// for(int x : nadj[i]) {
// cout << x << ' ';
// }
// cout << '\n';
// }
for(int i = 0; i < k; i++) {
vec.clear();
// cout << i + n << ' ' << "ok" << '\n';
dfs(n + i);
sort(vec.begin(), vec.end());
vec.erase(unique(vec.begin(), vec.end()), vec.end());
// for(int x : vec) cout << x << ' ';
// cout << '\n';
for(int x : nadj[n + i]) {
int mxx = 1, swp = 0;
for(int h : vec) {
if(h <= dis[x]) continue;
int l = lower_bound(lvl[h].begin(), lvl[h].end(), in[x]) - lvl[h].begin();
int r = upper_bound(lvl[h].begin(), lvl[h].end(), out[x]) - lvl[h].begin() - 1;
int mn = min((int)cnt[{h, c[x]}].size(), r - l + 1);
l = lower_bound(cnt[{h, c[x]}].begin(), cnt[{h, c[x]}].end(), in[x]) - cnt[{h, c[x]}].begin();
r = upper_bound(cnt[{h, c[x]}].begin(), cnt[{h, c[x]}].end(), out[x]) - cnt[{h, c[x]}].begin() - 1;
mxx += mn;
swp += (mn - (r - l + 1));
}
if(mxx > mx) {
mx = mxx;
sw = swp;
} else if(mxx == mx) sw = min(sw, swp);
}
}
cout << mx << ' ' << sw << '\n';
}
return 0;
}
