#include <bits/stdc++.h>
#define fi first
#define se second
#define pb push_back
#define eb emplace_back
using namespace std;
typedef long long LL;
typedef pair<int,int> pii;
typedef vector<int> vi;
template<class T> inline T re(){
T N = 0; char c = getchar(); bool neg = 0;
for (; c < '0' || c > '9'; c = getchar()) neg |= c == '-';
for (; c >= '0' && c <= '9'; c = getchar())
N = (N<<3)+(N<<1) + c - '0';
return neg ? -N : N;
}
const int SQRT = 325;
const int MX = 1e5;
int n, k;
int c[MX + 5], p[MX + 5], col_count[MX + 5];
int dep[MX + 5], dep_cnt[MX + 5], max_dep = 0;
vi chld[MX + 5], is_col[MX + 5], at_dep[MX + 5];
int cur_col[MX + 5]; // at each dep, # with current color
int cur_dep[MX + 5]; // current subtree, number of nodes at dep
int cur_at[MX + 5]; // current subtree, number of nodes at dep with current col
int ans_tot = 0, ans_moves = 0;
int flat[MX + 5], in_tme[MX + 5], out_tme[MX + 5];
void process_whole_tree(int col) { // do for big color
for (int i = 0; i < n; i++) {
if (c[i] == col) cur_col[dep[i]]++;
}
queue<int> q;
q.push(0);
while (!q.empty()) {
int u = q.front(); q.pop();
if (c[u] != col) {
for (int nx : chld[u]) {
q.push(nx);
}
} else {
// process subtree rooted at u
queue<int> tmp; tmp.push(u);
while (!tmp.empty()) {
int nx = tmp.front(); tmp.pop();
cur_dep[dep[nx]]++;
if (c[nx] == col) {
cur_at[dep[nx]]++;
}
for (int nxnx : chld[nx]) tmp.push(nxnx);
}
int moves = 0, cur_tot = 1; // start with 1 as root should be counted.
for (int i = dep[u] + 1; i <= max_dep; i++) {
int tmptmp = min(cur_dep[i], cur_col[i]);
cur_tot += tmptmp;
moves += tmptmp - cur_at[i];
}
if (cur_tot > ans_tot) {
ans_tot = cur_tot, ans_moves = moves;
} else if (cur_tot == ans_tot) {
ans_moves = min(ans_moves, moves);
}
cur_tot = 1, moves = 0;
tmp.push(u);
while (!tmp.empty()) {
int nx = tmp.front(); tmp.pop();
cur_dep[dep[nx]]--;
if (c[nx] == col) {
cur_at[dep[nx]]--;
}
for (int nxnx : chld[nx]) tmp.push(nxnx);
}
}
}
for (int i = 0; i < n; i++) {
if (c[i] == col) cur_col[dep[i]]--;
}
}
void process_small(int col) {
for (int x : is_col[col]) cur_col[dep[x]]++;
// cerr << "cur_col: "; for (int i = 0; i <= max_dep; i++) cerr << "(" << i << ": " << cur_col[i] << ") "; cerr << '\n';
// cerr << "elts: "; for (int i : is_col[col]) cerr << " " << i; cerr << '\n';
for (int rt : is_col[col]) {
int cur_tot = 1, moves = 0;
// cerr << "-- root " << rt << " --\n";
vi deps;
for (int nx : is_col[col]) {
if (nx == rt) continue;
deps.pb(dep[nx]);
if (in_tme[nx] >= in_tme[rt] && in_tme[nx] <= out_tme[rt]) cur_at[dep[nx]]++;
cur_dep[dep[nx]] = (
upper_bound(at_dep[dep[nx]].begin(), at_dep[dep[nx]].end(), flat[out_tme[rt]], [](int x, int y) {
return in_tme[x] < in_tme[y];
}) -
lower_bound(at_dep[dep[nx]].begin(), at_dep[dep[nx]].end(), rt, [](int x, int y) {
return in_tme[x] < in_tme[y];
})
);
}
sort(deps.begin(), deps.end());
deps.erase(unique(deps.begin(), deps.end()), deps.end());
// cerr << "cur_dep: "; for (int i = 0; i <= max_dep; i++) cerr << "(" << i << ": " << cur_dep[i] << ") "; cerr << '\n';
// cerr << "cur_at: "; for (int i = 0; i <= max_dep; i++) cerr << "(" << i << ": " << cur_at[i] << ") "; cerr << '\n';
// cerr << "deps: "; for (int i : deps) cerr << " " << i; cerr << '\n';
for (int dd : deps) {
if (dd > dep[rt]) {
int tmptmp = min(cur_dep[dd], cur_col[dd]);
cur_tot += tmptmp;
moves += tmptmp - cur_at[dd];
}
}
if (cur_tot > ans_tot) {
ans_tot = cur_tot, ans_moves = moves;
} else if (cur_tot == ans_tot) {
ans_moves = min(ans_moves, moves);
}
// cerr << "cur : " << cur_tot << ' ' << moves << '\n';
for (int nx : is_col[col]) {
if (nx == rt) continue;
if (in_tme[nx] >= in_tme[rt] && in_tme[nx] <= out_tme[rt]) cur_at[dep[nx]]--;
cur_dep[dep[nx]] = 0;
}
}
// cerr << "\n\n";
for (int x : is_col[col]) cur_col[dep[x]]--;
}
int main() {
/**
* for each node x, calculate:
* 1) number of nodes y with dep[y] > x with caveat each level has max card(z in subtree x with dep[z] fixed)
* 2) min number of swaps
*/
n = re<int>(); k = re<int>();
for (int i = 0; i < n; i++) {
col_count[c[i] = re<int>()]++;
is_col[c[i]].pb(i);
}
for (int i = 1; i < n; i++) {
p[i] = re<int>();
chld[p[i]].pb(i);
}
[&]() {
int _tme = 0;
function<void(int)> dfs_tme;
dfs_tme = [&](int u) -> void{
flat[++_tme] = u;
in_tme[u] = _tme;
max_dep = max(max_dep, dep[u]);
for (int nx : chld[u]) {
dep[nx] = dep[u] + 1;
dfs_tme(nx);
}
out_tme[u] = _tme;
};
dfs_tme(0);
} ();
for (int i = 0; i < n; i++) {
dep_cnt[dep[i]]++;
at_dep[dep[i]].pb(i);
}
for (int i = 0; i <= max_dep; i++) {
sort(at_dep[i].begin(), at_dep[i].end(), [](int x, int y) { return in_tme[x] < in_tme[y];});
}
for (int i = 0; i < k; i++) {
if (col_count[i] >= SQRT) process_whole_tree(i);
else process_small(i);
}
printf("%d %d\n", ans_tot, ans_moves);
return 0;
}
