#include <bits/stdc++.h>

using namespace std;

const int N = 1e5 + 10, M = 2010, B = 1600;

int n, k, a[N], dep[N], dfn[N], bk[N], tot, ans, ct, s[N], tp[N], t[N];
vector<int> g[N], p[N], col[N], c[N];

void dfs(int u, int fa) {
    dfn[u] = bk[u] = ++tot;
    dep[u] = dep[fa] + 1;
    for (int v : g[u]) {
        if (v != fa) {
            dfs(v, u), bk[u] = max(bk[u], bk[v]);
        }
    }
}

void dfs1(int u, int fa) {
    for (int v : g[u]) {
        if (v != fa) {
            dfs1(v, u);
            if (p[u].size() < p[v].size()) swap(p[u], p[v]);
            for (int i = p[u].size() - 1, j = p[v].size() - 1; j >= 0; i--, j--) {
                p[u][i] += p[v][j];
            }
        }
    }
    p[u].push_back(1);

    if (col[a[u]].size() <= B) {
        vector<int> tmp = p[u];
        int sum = 0, cnt = 0;
        for (int x : col[a[u]]) {
            int k = dep[x] - dep[u];
            if (k >= 0 && tmp[tmp.size() - 1 - k]) {
                tmp[tmp.size() - k - 1]--, sum++;
                cnt += dfn[u] <= dfn[x] && dfn[x] <= bk[u];
            }
        }
        if (ans < sum) ans = sum, ct = sum - cnt;
        else if (ans == sum) ct = min(ct, sum - cnt);
    }
}

void dfs2(int u, int fa, int Col) {
    for (int v : g[u]) {
        if (v != fa) {
            dfs2(v, u, Col);
            if (p[u].size() < p[v].size()) swap(p[u], p[v]), swap(s[u], s[v]), swap(c[u], c[v]), swap(t[u], t[v]);
            for (int i = p[u].size() - 1, j = p[v].size() - 1; j >= 0; i--, j--) {
                s[u] -= min(p[u][i], tp[dep[v] + p[u].size() - 1 - i]);
                p[u][i] += p[v][j], c[u][i] += c[v][j], t[u] += c[v][j];
                s[u] += min(p[u][i], tp[dep[v] + p[u].size() - 1 - i]);
            }
        }
    }
    p[u].push_back(1), c[u].push_back(a[u] == Col), s[u] += min(1, tp[dep[u]]);

    if (Col == a[u]) {
        t[u]++;
        //cout << u << ' ' << t[u] << ' ' << s[u] << '\n';
        if (ans < s[u]) ans = s[u], ct = s[u] - t[u];
        else if (ans == s[u]) ct = min(ct, s[u] - t[u]);
    }
}

int main() {
    ios::sync_with_stdio(0), cin.tie(0);
    cin >> n >> k;
    for (int i = 1; i <= n; i++) {
        cin >> a[i], col[a[i]].push_back(i);
    }
    for (int i = 2, fa; i <= n; i++) {
        cin >> fa, fa++, g[fa].push_back(i);
    }
    dfs(1, 0), dfs1(1, 0);
    for (int i = 0; i < k; i++) {
        if (col[i].size() >= B) {
            for (int j = 1; j <= n; j++) p[j].clear(), c[j].clear(), t[j] = s[j] = 0;
            for (int j = 1; j <= n; j++) if (a[j] == i) tp[dep[j]]++;
            dfs2(1, 0, i);
            fill(tp + 1, tp + n + 1, 0);
        }
    }
    cout << ans << ' ' << ct << '\n';
    return 0;
}