#include <iostream>
#include <vector>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <unordered_map>
#include <unordered_set>
#include <algorithm>
#include <deque>
#include <climits>
#include <cmath>
#include <numeric>
#include <string>
#include <bitset>
#include <assert.h>
#include <iomanip>
using namespace std;
template <typename T>
using pqg = priority_queue<T, vector<T>, greater<T>>;
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
template <typename T>
using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
const long long infl = 1e18 + 1;
const int inf = 1e9 + 1;
const int mod1 = 1e9 + 7;
const int mod2 = 998244353;
const long double eps = 1e-7;
const int mod = mod1;
int add(int a, int b) { return (a + b) % mod; }
int sub(int a, int b) { return (a - b + mod) % mod; }
int mul(int a, int b) { return (int)((long long)a * b % mod); }
int pwr(int a, int b = mod - 2)
{
int res = 1;
for(; b > 0; b >>= 1, a = mul(a, a))
if(b & 1)
res = mul(res, a);
return res;
}
void solve()
{
int n, k;
cin >> n >> k;
vector<int> c(n);
for(auto &i: c)
cin >> i;
vector adj(n, vector<int>());
for(int i = 1; i < n; i++)
{
int u;
cin >> u;
adj[u].push_back(i);
}
vector<int> dep(n, 0);
vector up(n, vector<int>(21, -1));
vector<vector<vector<int>>> children(n, vector<vector<int>>(21, vector<int>()));
auto dfs1 = [&](auto self, int u, int d) -> void
{
dep[u] = d++;
for(auto i: adj[u])
{
children[u][0].push_back(i);
up[i][0] = u;
self(self, i, d);
}
};
dfs1(dfs1, 0, 0);
for(int i = 1; i < 21; i++)
for(int j = 0; j < n; j++)
{
if(~up[j][i - 1])
up[j][i] = up[up[j][i - 1]][i - 1];
for(auto x: children[j][i - 1])
for(auto y: children[x][i - 1])
children[j][i].push_back(y);
}
auto get_kth_par = [&](int x, int k) -> int
{
for(int i = 0; i < 21; i++)
if((k >> i) & 1)
x = up[x][i];
return x;
};
auto get_kth_child = [&](int x, int k) -> int
{
vector<int> b{x};
for(int i = 0; i < 21; i++)
if((k >> i) & 1)
{
vector<int> c;
for(auto y: b)
{
for(auto z: children[y][i])
{
c.push_back(z);
}
}
b = c;
}
return (int)b.size();
};
vector b(k, vector<int>());
for(int i = 0; i < n; i++)
{
b[c[i]].push_back(i);
}
int mx = 0, mn = 0;
for(auto ar: b)
{
int m = (int)ar.size();
int mxx = inf, idx = 0;
for(int i = 0; i < m; i++)
if(dep[ar[i]] < mxx)
mxx = dep[ar[i]], idx = ar[i];
map<int, vector<int>> mp;
vector<int> oo;
for(int j = 0; j < m; j++)
{
if(dep[ar[j]] == dep[idx])
{
oo.push_back(ar[j]);
continue;
}
mp[dep[ar[j]]].push_back(ar[j]);
}
for(auto o: oo)
{
int curr1 = 1, curr2 = 0;
for(auto [f, s]: mp)
{
int mxxx = get_kth_child(o, f - mxx);
// cout << o << ' ' << mxx << ' ' << f << ' ' << f - mxx << '\n';
int have = 0;
int all = (int)s.size();
for(auto y: s)
if(get_kth_par(y, f - mxx) == o)
have++;
curr2 += min(all - have, mxxx - have);
curr1 += min(all, mxxx);
}
if(curr1 > mx)
{
mx = curr1;
mn = curr2;
}
else if(curr1 == mx)
mn = min(mn, curr2);
}
}
cout << mx << ' ' << mn;
}
int main()
{
ios::sync_with_stdio(false);
cin.tie(nullptr);
int t = 1;
// cin >> t;
while (t--) {
solve();
cout << (t ? "\n" : "");
}
}
