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.math.BigDecimal;
import java.math.BigInteger;
import java.util.*;


public class Main {


    public static Edge[] edges;
    public static int[] treeSize;
    public static int[] root;
    public static long[] count;

    public static int rootOfTreeU;
    public static int rootOfTreeV;

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        solve(in, out);
        out.close();
    }

    public static void solve(InputReader in, PrintWriter out) {

        int n = in.nextInt();
        int m = in.nextInt();
        if(n == 1){
            for(int i = 0; i < m; i++){
                int q = in.nextInt();
                out.println(0);
            }
        }else {

            edges = new Edge[n - 1];
            for (int i = 0; i < n - 1; i++) {
                Edge edge = new Edge(in.nextInt(), in.nextInt(), in.nextInt());
                edges[i] = edge;
            }
            treeSize = new int[n + 10];
            root = new int[n + 10];
            for (int i = 1; i <= n; i++) {
                treeSize[i] = 1;
                root[i] = i;
            }

            Arrays.sort(edges);

            int maxWeight = edges[edges.length - 1].weight + 10;
            count = new long[maxWeight];
            for (Edge edge : edges) {
                rootOfTreeU = findRoot(edge.node1);
                rootOfTreeV = findRoot(edge.node2);

                root[rootOfTreeU] = rootOfTreeV;
                count[edge.weight] += (long) treeSize[rootOfTreeU] * treeSize[rootOfTreeV];
                treeSize[rootOfTreeV] += treeSize[rootOfTreeU];
            }

            for (int i = 1; i < count.length; i++) {
                count[i] += count[i - 1];
            }

            StringBuilder ans = new StringBuilder();
            for (int i = 0; i < m - 1; i++) {
                ans.append(count[Math.min(in.nextInt(), count.length - 1)]).append(" ");
            }
            ans.append(count[Math.min(in.nextInt(), count.length - 1)]);
            out.println(ans);
        }
    }


    public static int findRoot(int x) {
        if (root[x] == x) {
            return x;
        } else {
            int x1 = findRoot(root[x]);
            root[x] = x1;
            return x1;
        }
    }


    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

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

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

        public char[] nextCharArray() {
            return next().toCharArray();
        }

        public boolean hasNext() {
            try {
                String string = reader.readLine();
                if (string == null) {
                    return false;
                }
                tokenizer = new StringTokenizer(string);
                return tokenizer.hasMoreTokens();
            } catch (IOException e) {
                return false;
            }
        }

        public BigInteger nextBigInteger() {
            return new BigInteger(next());
        }

        public BigDecimal nextBigDecinal() {
            return new BigDecimal(next());
        }
    }

}

class Edge implements Comparable<Edge> {
    int node1;
    int node2;
    int weight;

    public Edge(int node1, int node2, int weight) {
        this.node1 = node1;
        this.node2 = node2;
        this.weight = weight;
    }


    @Override
    public int compareTo(Edge o) {
        return this.weight - o.weight;
    }
}