#include <bits/stdc++.h>
using namespace std;
void dfs(long long x, vector<vector<long long>> &AR, vector<long long> &depth, long long cur)
{
depth[x] = cur;
for (long long i = 0; i < AR[x].size(); i++)
{
dfs(AR[x][i], AR, depth, cur + 1);
}
}
void dfs2(long long x, vector<vector<long long>> &AR, vector<vector<pair<long long, long long>>> &colorpos, vector<long long> &available, map<long long, long long> &M, vector<long long> &C, vector<vector<long long>> &colors, long long cur, long long &best, long long &best2)
{
available.push_back(1);
vector<long long> available2;
map<long long, long long> M2;
M[C[x]] += 1;
for (long long i = 0; i < AR[x].size(); i++)
{
available2.clear();
M2.clear();
dfs2(AR[x][i], AR, colorpos, available2, M2, C, colors, cur + 1, best, best2);
available2.push_back(0);
if (available2.size() > available.size())
swap(available2, available);
for (long long j = 0; j < available2.size(); j++)
{
available[j + available.size() - available2.size()] += available2[j];
}
if (M2.size() > M.size())
swap(M, M2);
for (auto j : M2)
{
M[j.first] += j.second;
}
}
if (colors[C[x]].size() <= sqrt(AR.size()))
{
long long ans1 = 0, ans2 = 0;
for (long long i = 0; i < colorpos[C[x]].size(); i++)
{
if (colorpos[C[x]][i].first >= cur && colorpos[C[x]][i].first < cur + available.size())
ans1 += min(colorpos[C[x]][i].second, available[available.size() - colorpos[C[x]][i].first - 1 + cur]);
}
ans2 = ans1 - M[C[x]];
if (ans1 > best || (ans1 == best && ans2 < best2))
{
best = ans1, best2 = ans2;
}
}
}
pair<long long, long long> dfs3(long long x, vector<vector<long long>> &AR, vector<long long> &C, long long c, vector<long long> &used, vector<long long> &maxx, long long cur, long long &best, long long &best2)
{
vector<long long> used2;
long long tot = 0, tot2 = 0;
if (C[x] == c)
tot2++;
used.push_back(0);
if (maxx[cur] != 0)
{
used[0] = 1;
tot++;
}
for (long long i = 0; i < AR[x].size(); i++)
{
used2.clear();
pair<long long, long long> temp = dfs3(AR[x][i], AR, C, c, used2, maxx, cur + 1, best, best2);
tot2 += temp.second;
used2.push_back(0);
if (used2.size() > used.size())
{
swap(used2, used);
swap(tot, temp.first);
}
for (long long j = 0; j < used2.size(); j++)
{
tot -= used[j + used.size() - used2.size()];
used[j + used.size() - used2.size()] = min(used[j + used.size() - used2.size()] + used2[j], maxx[cur + used2.size() - j - 1]);
tot += used[j + used.size() - used2.size()];
}
}
if (C[x] == c && (tot > best || (tot == best && tot2 < best2)))
{
best = tot, best2 = tot - tot2;
}
return {tot, tot2};
}
int main()
{
cin.tie(0);
cout.tie(0);
ios_base::sync_with_stdio(0);
long long N, K;
cin >> N >> K;
vector<long long> C(N);
vector<vector<long long>> colors(K);
for (long long i = 0; i < N; i++)
{
cin >> C[i];
colors[C[i]].push_back(i);
}
vector<long long> p(N, 0);
vector<vector<long long>> AR(N);
for (long long i = 1; i < N; i++)
{
cin >> p[i];
AR[p[i]].push_back(i);
}
vector<long long> depth(N);
vector<vector<pair<long long, long long>>> colorpos(K);
dfs(0, AR, depth, 0);
long long best = 0, best2 = 0;
for (long long i = 0; i < K; i++)
{
for (long long j = 0; j < colors[i].size(); j++)
{
colorpos[i].push_back({depth[colors[i][j]], 1});
}
sort(colorpos[i].begin(), colorpos[i].end());
vector<pair<long long, long long>> temp;
long long cur = 0;
for (long long j = 0; j < colors[i].size(); j++)
{
if (j > 0 && colorpos[i][j].first != colorpos[i][j - 1].first)
{
temp.push_back({colorpos[i][j - 1].first, cur});
cur = 0;
}
cur++;
}
if (colors[i].size() > 0)
temp.push_back({colorpos[i].back().first, cur});
swap(temp, colorpos[i]);
}
vector<long long> available;
map<long long, long long> M;
dfs2(0, AR, colorpos, available, M, C, colors, 0, best, best2);
for (long long i = 0; i < K; i++)
{
if (colors[i].size() >= sqrt(N) - 1)
{
vector<long long> used, maxx(N);
for (long long j = 0; j < colors[i].size(); j++)
maxx[depth[colors[i][j]]]++;
pair<long long, long long> temp = dfs3(0, AR, C, i, used, maxx, 0, best, best2);
}
}
cout << best << ' ' << best2;
}
