You are given m sets of integers A_1, A_2, …, A_m; elements of these sets are integers between 1 and n, inclusive.

There are two arrays of positive integers a_1, a_2, …, a_m and b_1, b_2, …, b_n. 

In one operation you can delete an element j from the set A_i and pay a_i + b_j coins for that.

You can make several (maybe none) operations (some sets can become empty).

After that, you will make an edge-colored undirected graph consisting of n vertices. For each set A_i you will add an edge (x, y) with color i for all x, y ∈ A_i and x < y. Some pairs of vertices can be connected with more than one edge, but such edges have different colors.

You call a cycle i_1 → e_1 → i_2 → e_2 → … → i_k → e_k → i_1 (e_j is some edge connecting vertices i_j and i_{j+1} in this graph) rainbow if all edges on it have different colors.

Find the minimum number of coins you should pay to get a graph without rainbow cycles.

Input

The first line contains two integers m and n (1 ≤ m, n ≤ 10^5), the number of sets and the number of vertices in the graph.

The second line contains m integers a_1, a_2, …, a_m (1 ≤ a_i ≤ 10^9).

The third line contains n integers b_1, b_2, …, b_n (1 ≤ b_i ≤ 10^9).

In the each of the next of m lines there are descriptions of sets. In the i-th line the first integer s_i (1 ≤ s_i ≤ n) is equal to the size of A_i. Then s_i integers follow: the elements of the set A_i. These integers are from 1 to n and distinct.

It is guaranteed that the sum of s_i for all 1 ≤ i ≤ m does not exceed 2 ⋅ 10^5.

Output

Print one integer: the minimum number of coins you should pay for operations to avoid rainbow cycles in the obtained graph.

Examples

Input


3 2
1 2 3
4 5
2 1 2
2 1 2
2 1 2


Output


11


Input


7 8
3 6 7 9 10 7 239
8 1 9 7 10 2 6 239
3 2 1 3
2 4 1
3 1 3 7
2 4 3
5 3 4 5 6 7
2 5 7
1 8


Output


66

Note

In the first test, you can make such operations:

  * Delete element 1 from set 1. You should pay a_1 + b_1 = 5 coins for that. 
  * Delete element 1 from set 2. You should pay a_2 + b_1 = 6 coins for that. 



You pay 11 coins in total. After these operations, the first and the second sets will be equal to \{2\} and the third set will be equal to \{1, 2\}.

So, the graph will consist of one edge (1, 2) of color 3.

In the second test, you can make such operations:

  * Delete element 1 from set 1. You should pay a_1 + b_1 = 11 coins for that. 
  * Delete element 4 from set 2. You should pay a_2 + b_4 = 13 coins for that. 
  * Delete element 7 from set 3. You should pay a_3 + b_7 = 13 coins for that. 
  * Delete element 4 from set 4. You should pay a_4 + b_4 = 16 coins for that. 
  * Delete element 7 from set 6. You should pay a_6 + b_7 = 13 coins for that. 



You pay 66 coins in total.

After these operations, the sets will be:

  * \{2, 3\}; 
  * \{1\}; 
  * \{1, 3\}; 
  * \{3\}; 
  * \{3, 4, 5, 6, 7\}; 
  * \{5\}; 
  * \{8\}. 



We will get the graph:

<image>

There are no rainbow cycles in it.
import java.io.*;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Random;
import java.util.StringTokenizer;

public class E {
    //Solution by Sathvik Kuthuru
    public static void main(String[] args) {
        FastReader scan = new FastReader();
        PrintWriter out = new PrintWriter(System.out);
        Task solver = new Task();
        int t = 1;
        for(int tt = 1; tt <= t; tt++) solver.solve(tt, scan, out);
        out.close();
    }

    static class Task {
        int n, m;
        long[] a, b;
        ArrayList<Edge> edges;

        public void solve(int testNumber, FastReader scan, PrintWriter out) {
            m = scan.nextInt();
            n = scan.nextInt();
            a = new long[m];
            b = new long[n];
            edges = new ArrayList<>();
            DSU set = new DSU(n + m);
            long total = 0;

            for(int i = 0; i < m; i++) a[i] = scan.nextLong();
            for(int i = 0; i < n; i++) b[i] = scan.nextLong();
            for(int i = 0; i < m; i++) {
                int size = scan.nextInt();
                for(int j = 0; j < size; j++) {
                    int curr = scan.nextInt() - 1;
                    edges.add(new Edge(curr,  n + i, a[i] + b[curr]));
                    total += a[i] + b[curr];
                }
            }
            Collections.sort(edges);
            Collections.reverse(edges);
            long ans = 0;
            for(Edge e : edges) {
                if(set.unite(e.from, e.to)) {
                    ans += e.weight;
                }
                else {
                    //out.printf("Deleted: Set: %d, Item: %d\n", e.to - n + 1, e.from + 1);
                }
            }
            out.println(total - ans);
        }

        static class DSU {
            int n;
            int[] parent, size;

            public DSU(int v) {
                n = v;
                parent = new int[n];
                size = new int[n];
                for(int i = 0; i < n; i++) {
                    parent[i] = i;
                    size[i] = 1;
                }
            }

            public int findRoot(int curr) {
                if(curr == parent[curr]) return curr;
                return parent[curr] = findRoot(parent[curr]);
            }

            public boolean unite(int a, int b) {
                int rootA = findRoot(a);
                int rootB = findRoot(b);
                if(rootA == rootB) return false;
                if(size[rootA] > size[rootB]) {
                    parent[rootB] = rootA;
                    size[rootA] += size[rootB];
                }
                else {
                    parent[rootA] = rootB;
                    size[rootB] += size[rootA];
                }
                return true;
            }

        }

        static class Edge implements Comparable<Edge> {
            int from, to;
            long weight;

            public Edge(int x, int a, long b) {
                from = x;
                to = a;
                weight = b;
            }

            @Override
            public int compareTo(Edge edge) {
                return Long.compare(weight, edge.weight);
            }
        }

    }

    static void shuffle(int[] a) {
        Random get = new Random();
        for (int i = 0; i < a.length; i++) {
            int r = get.nextInt(a.length);
            int temp = a[i];
            a[i] = a[r];
            a[r] = temp;
        }
    }

    static void shuffle(long[] a) {
        Random get = new Random();
        for (int i = 0; i < a.length; i++) {
            int r = get.nextInt(a.length);
            long temp = a[i];
            a[i] = a[r];
            a[r] = temp;
        }
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public FastReader(String s) throws FileNotFoundException {
            br = new BufferedReader(new FileReader(new File(s)));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

}