#include <bits/stdc++.h>
using namespace std;
void dfs(int x, int p, vector<vector<int>> &sons, vector<int> &depth, int prof, vector<vector<int>> &lca)
{
depth[x] = prof;
lca[0][x] = p;
for (int i = 0; i < sons[x].size(); i++)
{
dfs(sons[x][i], x, sons, depth, prof + 1, lca);
}
}
void dfs2(int x, vector<vector<int>> &sons, vector<int> &Tab, vector<vector<pair<int, int>>> &colors, vector<vector<pair<int, int>>> &sub, vector<pair<int, int>> &ans, vector<int> &big, vector<map<int, int>> &M, map<int, int> &space, vector<int> &num, vector<int> &swaps, vector<vector<int>> &precalc, vector<vector<int>> &taken, int prof)
{
map<int, int> space2;
space2[prof]++;
vector<int> num2(big.size()), swaps2(big.size());
vector<map<int, int>> M2(big.size());
if (colors[Tab[x]].size() > sqrt(sons.size()))
{
int temp = lower_bound(big.begin(), big.end(), Tab[x]) - big.begin();
M2[temp][prof]++;
num2[temp]++;
}
for (int i = 0; i < big.size(); i++)
{
swaps2[i] -= num2[i];
num2[i] = min(precalc[i][prof], space2[prof]);
swaps2[i] += num2[i];
}
for (int i = 0; i < sons[x].size(); i++)
{
dfs2(sons[x][i], sons, Tab, colors, sub, ans, big, M, space, num, swaps, precalc, taken, prof + 1);
if (space.size() > space2.size())
{
swap(space, space2);
swap(M, M2);
swap(num, num2);
swap(swaps, swaps2);
}
for (auto val : space)
{
for (int j = 0; j < big.size(); j++)
{
swaps2[j] -= min(space2[val.first], precalc[j][val.first]) - M2[j][val.first];
num2[j] -= min(space2[val.first], precalc[j][val.first]);
num2[j] += min(space2[val.first] + val.second, precalc[j][val.first]);
swaps2[j] += min(space2[val.first] + val.second, precalc[j][val.first]) - M2[j][val.first] - M[j][val.first];
if (M2[j][val.first] == 0)
M2[j].erase(val.first);
if (M[j][val.first] == 0)
M[j].erase(val.first);
}
space2[val.first] += val.second;
}
for (int j = 0; j < big.size(); j++)
{
for (auto val : M[j])
{
M2[j][val.first] += val.second;
}
}
}
if (colors[Tab[x]].size() > sqrt(sons.size()))
{
int temp = lower_bound(big.begin(), big.end(), Tab[x]) - big.begin();
ans[x] = {num2[temp], swaps2[temp]};
}
else
{
for (int i = 0; i < taken[x].size(); i++)
space2[taken[x][i]]--;
for (int i = 0; i < sub[x].size(); i++)
{
space2[sub[x][i].first]--;
if (space2[sub[x][i].first] >= 0)
{
ans[x].first++;
ans[x].second++;
}
}
for (int i = 0; i < sub[x].size(); i++)
{
space2[sub[x][i].first]++;
if (space2[sub[x][i].first] == 0)
space2.erase(sub[x][i].first);
}
for (int i = 0; i < taken[x].size(); i++)
{
space2[taken[x][i]]++;
if (space2[taken[x][i]] == 0)
space2.erase(taken[x][i]);
}
}
swap(M, M2);
swap(space, space2);
swap(num, num2);
swap(swaps, swaps2);
}
int main()
{
cin.tie(0);
cout.tie(0);
ios_base::sync_with_stdio(0);
int N, K;
cin >> N >> K;
vector<int> Tab(N);
vector<vector<pair<int, int>>> colors(K);
for (int i = 0; i < N; i++)
{
cin >> Tab[i];
colors[Tab[i]].push_back({0, i});
}
vector<int> big, small;
for (int i = 0; i < K; i++)
if (colors[i].size() > sqrt(N))
big.push_back(i);
else
small.push_back(i);
vector<vector<int>> sons(N);
for (int i = 0; i < N - 1; i++)
{
int x;
cin >> x;
sons[x].push_back(i + 1);
}
vector<int> depth(N);
vector<vector<int>> lca(log2(N) + 1, vector<int>(N));
dfs(0, 0, sons, depth, 0, lca);
for (int i = 1; i <= log2(N); i++)
{
for (int j = 0; j < N; j++)
{
lca[i][j] = lca[i - 1][lca[i - 1][j]];
}
}
for (int i = 0; i < K; i++)
{
for (int j = 0; j < colors[i].size(); j++)
{
colors[i][j].first = depth[colors[i][j].second];
}
sort(colors[i].begin(), colors[i].end());
}
vector<vector<pair<int, int>>> sub(N);
vector<vector<int>> taken(N);
vector<pair<int, int>> ans(N);
for (int i = 0; i < small.size(); i++)
{
int cur = small[i];
for (int j = 0; j < colors[cur].size(); j++)
{
ans[colors[cur][j].second].first++;
for (int k = 0; k < colors[cur].size(); k++)
{
if (colors[cur][k].first == colors[cur][j].first)
break;
int a = colors[cur][j].second;
for (int l = log2(N); l >= 0; l--)
if (depth[lca[l][a]] >= depth[colors[cur][k].second])
a = lca[l][a];
if (a == colors[cur][k].second)
{
ans[colors[cur][k].second].first++;
taken[colors[cur][k].second].push_back(colors[cur][j].first);
continue;
}
sub[colors[cur][k].second].push_back(colors[cur][j]);
}
}
}
vector<map<int, int>> M(big.size());
map<int, int> space;
vector<int> num(big.size()), swaps(big.size());
vector<vector<int>> precalc(big.size(), vector<int>(N));
for (int i = 0; i < big.size(); i++)
{
for (int j = 0; j < colors[big[i]].size(); j++)
{
precalc[i][colors[big[i]][j].first]++;
}
}
dfs2(0, sons, Tab, colors, sub, ans, big, M, space, num, swaps, precalc, taken, 0);
int best = 0, best2 = 0;
for (int i = 0; i < N; i++)
{
if (ans[i].first > best || (ans[i].first == best && ans[i].second < best2))
{
best = ans[i].first;
best2 = ans[i].second;
}
}
cout << best << ' ' << best2;
}
