#include <bits/stdc++.h>
using namespace std;

const int N = 1e5 + 10, B = 350;

int n, k, c[N], p[N], dep[N];
vector<int> d[N], g[N], lang[N];
map<int, int> mp[N];
int tmp[N], dc[N], sc[N];
pair<int, int> ans;

void dfsDep(int u) {
    for(int v : g[u]) {
        dep[v] = dep[u] + 1;
        dfsDep(v);
    }
}

void dfs(int u) {
    for(int v : g[u]) {
        dfs(v);
        if(d[u].size() < d[v].size()) swap(d[u], d[v]);
        for(int i = 1; i <= d[v].size(); i ++)
            *(d[u].end() - i) += *(d[v].end() - i);
        
        if(mp[u].size() < mp[v].size()) swap(mp[u], mp[v]);
        for(auto [a, b] : mp[v])
            mp[u][a] += b;
    }
    d[u].push_back(1);
    sc[u] = ++ mp[u][c[u]];

    //cout << u << ": ";
    //for(int x : d[u]) cout << x << " ";

    if(lang[c[u]].size() < B) {
        int sum = 0;
        for(int v : lang[c[u]])
            if(dep[v] >= dep[u]) {
                tmp[dep[v] - dep[u]] ++;
                if(dep[v] - dep[u] < d[u].size() && tmp[dep[v] - dep[u]] <= *(d[u].rbegin() + (dep[v] - dep[u]))) sum ++;
            }
        //cout << "sum = " << sum << "\n";
        ans = max(ans, make_pair(sum, sum - sc[u]));
        for(int v : lang[c[u]])
            if(dep[v] >= dep[u])
                tmp[dep[v] - dep[u]] --;
    }
}

int dfs(int u, int col) {
    int ret = 0;
    for(int v : g[u]) {
        int x = dfs(v, col);
        if(d[v].size() > d[u].size()) {
            swap(ret, x);
            swap(d[u], d[v]);
        }
        for(int i = 1; i <= d[v].size(); i ++) {
            if(dc[dep[u] + i] > *(d[u].end() - i)) ret += min(*(d[v].end() - i), dc[dep[u] + i] - *(d[u].end() - i));
            *(d[u].end() - i) += *(d[v].end() - i);
        }
    }
    d[u].push_back(1);
    ret += (dc[dep[u]] > 0);
    if(c[u] == col) ans = max(ans, make_pair(ret, ret - sc[u]));
    return ret;
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);

    cin >> n >> k;
    
    for(int i = 0; i < n; i ++) {
        cin >> c[i];
        lang[c[i]].push_back(i);
    }

    for(int i = 1; i < n; i ++) {
        cin >> p[i];
        g[p[i]].push_back(i);
    }
    
    dfsDep(0);
    dfs(0);

    for(int i = 0; i < k; i ++) {
        if(lang[i].size() >= B) {
            memset(dc, 0, sizeof dc);
            for(int u : lang[i])
                dc[dep[u]] ++;
            for(int i = 0; i < n; i ++)
                d[i].clear();
            dfs(0, i);
        }
    }

    cout << ans.first << " " << ans.second;
}