COUNTPROBS

#define task "COUNTPROBS"
#include <iostream>
#include <cstdio>
#include <vector>
#include <cassert>

using namespace std;

using ll = long long;
using ld = long double;

template <class T>
void read(T &x)
{
    x = 0;
    register int c;

    while ((c = getchar()) && (c > '9' || c < '0'))
        ;
    for (; c >= '0' && c <= '9'; c = getchar())
        x = x * 10 + c - '0';
}

constexpr int N = 1e6 + 5;
int n, m, l;
vector<int> goodat[N], adj[N];
vector<int> allvers[N * 3];
int x[N * 2][21], ranks[N];
int sumup[N], in[N];

void Read()
{
    // assert(cin >> n >> m);
    read(n), read(m);

    for (int i = 1; i <= n; ++i)
    {
        int t;
        // assert(cin >> t);
        read(t);

        goodat[i].resize(t);

        for (auto &j : goodat[i])
            // assert(cin >> j);
            read(j);
    }

    for (int i = 2; i <= n; ++i)
    {
        int p;
        // assert(cin >> p);
        read(p);

        adj[p].emplace_back(i);
    }
}

void dfs(int v)
{
    x[in[v] = ++l][0] = v;

    for (int i : adj[v])
    {
        ranks[i] = ranks[v] + 1;
        dfs(i);
        x[++l][0] = v;
    }
}

int LCA(int u, int v)
{
    int l = in[u], r = in[v];
    if (l > r)
        swap(l, r);

    int loga = __lg(r - l + 1);

    if (ranks[x[l][loga]] < ranks[x[r - (1 << loga) + 1][loga]])
        return x[l][loga];

    return x[r - (1 << loga) + 1][loga];
}

void Solve()
{
    ranks[1] = 1;
    dfs(1);

    for (int i = l; i; --i)
        if (i == in[x[i][0]])
            for (auto j : goodat[x[i][0]])
                allvers[j].emplace_back(x[i][0]);

    // LCA O(1)
    for (int i = 1; i < 21; ++i)
        for (int j = 1; j <= l - (1 << i) + 1; ++j)
            x[j][i] = (ranks[x[j][i - 1]] < ranks[x[j + (1 << (i - 1))][i - 1]] ? x[j][i - 1] : x[j + (1 << (i - 1))][i - 1]);

    for (int i = 1; i <= m; ++i)
    {
        for (int j = 0; j < (int)allvers[i].size(); ++j)
        {
            ++sumup[allvers[i][j]];

            if (j != (int)allvers[i].size() - 1)
                --sumup[LCA(allvers[i][j], allvers[i][j + 1])];
        }
    }

    for (int i = l; i; --i)
        if (i == in[x[i][0]])
            for (auto j : adj[x[i][0]])
                sumup[x[i][0]] += sumup[j];

    for (int i = 1; i <= n; ++i)
        cout << sumup[i] << " ";
}

int32_t main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);

    if (fopen(task ".INP", "r"))
    {
        freopen(task ".INP", "r", stdin);
        freopen(task ".OUT", "w", stdout);
    }

    Read();
    Solve();
}