#include <bits/stdc++.h>

using i64 = long long;
using u64 = unsigned long long;
using u32 = unsigned;

int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    
    int N, K;
    std::cin >> N >> K;
    
    std::vector<int> l(N);
    for (int i = 0; i < N; i++) {
        std::cin >> l[i];
    }
    
    std::vector<std::vector<int>> adj(N);
    std::vector<int> b(N);
    b[0] = -1;
    for (int i = 1; i < N; i++) {
        std::cin >> b[i];
        adj[b[i]].push_back(i); 
    }
    
    std::vector<std::vector<int>> vec(K);
    for (int i = 0; i < N; i++) {
        vec[l[i]].push_back(i);
    }
    
    std::vector<int> cnt(N), in(N, -1), out(N), ord(N), h(N), dep(N);
    int cur = 0;
    auto dfs1 = [&](auto &self, int x) -> void {
        for (auto &y : adj[x]) {
            dep[y] = dep[x] + 1;
            self(self, y);
            h[x] = std::max(h[x], h[y] + 1);
            if (h[y] > h[adj[x][0]]) {
                std::swap(y, adj[x][0]);
            }
        }
    };
    dfs1(dfs1, 0);
    
    std::vector<int> tmp(N);
    
    int P = 0, S = 0;
    auto dfs2 = [&](auto &self, int x) -> void {
        in[x] = cur++;
        ord[in[x]] = x;
        for (auto y : adj[x]) {
            self(self, y);
            if (y != adj[x][0]) {
                for (int i = 0; i <= h[y]; i++) {
                    cnt[in[x] + 1 + i] += cnt[in[y] + i];
                }
            }
        }
        out[x] = cur;
        cnt[in[x]]++;
        int p = 1, s = 0;
        for (auto v : vec[l[x]]) {
            if (in[x] <= in[v] && in[v] < out[x]) {
                s++;
            }
            if (dep[v] > dep[x] && dep[v] <= dep[x] + h[x]) {
                tmp[dep[v]]++;
            }
        }
        for (auto v : vec[l[x]]) {
            if (tmp[dep[v]] > 0) {
                p += std::min(tmp[dep[v]], cnt[in[x] + dep[v] - dep[x]]);
                tmp[dep[v]] = 0;
            }
        }
        s = p - s;
        if (p > P || (p == P && s < S)) {
            P = p;
            S = s;
        }
    };
    dfs2(dfs2, 0);
    
    std::cout << P << " " << S << "\n";
    
    return 0;
}