Problem: You are given a weighted tree consisting of n vertices. Recall that a tree is a connected graph without cycles. Vertices u_i and v_i are connected by an edge with weight w_i.

You are given m queries. The i-th query is given as an integer q_i. In this query you need to calculate the number of pairs of vertices (u, v) (u < v) such that the maximum weight of an edge on a simple path between u and v doesn't exceed q_i.

Input

The first line of the input contains two integers n and m (1 ≤ n, m ≤ 2 ⋅ 10^5) — the number of vertices in the tree and the number of queries.

Each of the next n - 1 lines describes an edge of the tree. Edge i is denoted by three integers u_i, v_i and w_i — the labels of vertices it connects (1 ≤ u_i, v_i ≤ n, u_i ≠ v_i) and the weight of the edge (1 ≤ w_i ≤ 2 ⋅ 10^5). It is guaranteed that the given edges form a tree.

The last line of the input contains m integers q_1, q_2, ..., q_m (1 ≤ q_i ≤ 2 ⋅ 10^5), where q_i is the maximum weight of an edge in the i-th query.

Output

Print m integers — the answers to the queries. The i-th value should be equal to the number of pairs of vertices (u, v) (u < v) such that the maximum weight of an edge on a simple path between u and v doesn't exceed q_i.

Queries are numbered from 1 to m in the order of the input.

Examples

Input


7 5
1 2 1
3 2 3
2 4 1
4 5 2
5 7 4
3 6 2
5 2 3 4 1


Output


21 7 15 21 3 


Input


1 2
1 2


Output


0 0 


Input


3 3
1 2 1
2 3 2
1 3 2


Output


1 3 3 

Note

The picture shows the tree from the first example: <image>

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class G
{
    PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
    BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
    StringTokenizer tok;

    public void go() throws IOException
    {
        ntok();
        int n = ipar();
        int m = ipar();
        int[][] edges = new int[n-1][];
        for (int i = 0; i < n-1; i++)
        {
            ntok();
            edges[i] = new int[] {ipar(), ipar(), ipar()};
        }
        long[][] queries = new long[m][3];
        ntok();
        for (int i = 0; i < m; i++)
        {
            queries[i][0] = ipar();
            queries[i][1] = i;
        }
        Arrays.sort(edges, (a, b) -> Integer.compare(a[2], b[2]));
        Arrays.sort(queries, (a, b) -> Long.compare(a[0], b[0]));
        long total = 0;
        int q = 0;
        UnionFind uf = new UnionFind(n);
        OUTER:
        for (int[] edge : edges)
        {
            while (edge[2] > queries[q][0])
            {
                queries[q][2] = total;
                q++;
                if (q == m)
                {
                    break OUTER;
                }
            }
            int i = uf.find(edge[0]-1);
            int j = uf.find(edge[1]-1);
            if (i != j)
            {
                total += uf.sz[i] * uf.sz[j];
                uf.union(i, j);
            }
        }
        while (q < m)
        {
            queries[q][2] = total;
            q++;
        }
        Arrays.sort(queries, (a, b) -> Long.compare(a[1], b[1]));
        for (int i = 0; i < m; i++)
        {
            if (i != 0)
            {
                out.print(" ");
            }
            out.print(queries[i][2]);
        }
        out.println();

        out.flush();
        in.close();
    }

    private class UnionFind
    {
        int[] arr;
        long[] sz; 
        
        public UnionFind(int n)
        {
            arr = new int[n];
            sz = new long[n];
            for (int i = 0; i < n; i++)
            {
                arr[i] = i;
                sz[i] = 1;
            }
        }

        public void union(int i, int j)
        {
            i = find(i);
            j = find(j);
            if (sz[j] > sz[i])
            {
                int temp = i;
                i = j;
                j = temp;
            }
            arr[j] = i;
            sz[i] += sz[j];
        }

        public int find(int i)
        {
            return (arr[i] = arr[i] == i ? i : find(arr[i]));
        }
    }

    public void ntok() throws IOException
    {
        tok = new StringTokenizer(in.readLine());
    }

    public int ipar()
    {
        return Integer.parseInt(tok.nextToken());
    }

    public long lpar()
    {
        return Long.parseLong(tok.nextToken());
    }

    public double dpar()
    {
        return Double.parseDouble(tok.nextToken());
    }

    public String spar()
    {
        return tok.nextToken();
    }

    public static void main(String[] args) throws IOException
    {
        new G().go();
    }
}