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 lab10B {

    //static int[] fa;
    static Node[] nodeList;
    static Edge[] edgeList;

    public static void main(String[] args) throws IOException {
        Reader in = new Reader();
        PrintWriter out = new PrintWriter(System.out);
        long n = in.nextInt();
        int m = in.nextInt(), u, v, w, q, maxW = 0, lu, lv, w1;
        long maxAnswer = n * (n - 1) / 2;

        //fa = new int[n + 1];//from 1
        nodeList = new Node[(int) (n + 1)];
        edgeList = new Edge[(int) (n - 1)];
        int[] query = new int[m];
        long[] count = new long[200001]; //from 1
        //nodeList[0] = new Node(-1);
        for (int i = 1; i <= n; i++) {
            nodeList[i] = new Node(i);
        }
        for (int i = 0; i < n - 1; i++) {
            u = in.nextInt();
            v = in.nextInt();
            w = in.nextInt();
            edgeList[i] = new Edge(u, v, w);
            nodeList[u].connections.add(edgeList[i]);
            nodeList[v].connections.add(edgeList[i]);
            maxW = Math.max(maxW, w);
        }
        for (int i = 0; i < m; i++) {
            query[i] = in.nextInt();
        }

        Arrays.sort(edgeList, Comparator.comparingLong(o -> o.weight));
        //Node nodeU, nodeV;
        for (int i = 0; i < n - 1; i++) {
            u = edgeList[i].u;
            v = edgeList[i].v;
            w = edgeList[i].weight;
            lu = find(u);
            lv = find(v);
            if (lu != lv) {
                if (count[w] == 0) {
                    w1 = w - 1;
                    while (w1 > 0 && count[w1] == 0) {
                        w1--;
                    }
                    for (int j = 1; w1 + j <= w; j++) {
                        count[w1 + j] = count[w1];
                    }
                }
                count[w] = count[w] + nodeList[lu].num * nodeList[lv].num;
                union(lu, lv);
            }
        }

        q = query[0];
        out.print((q >= maxW) ? maxAnswer : count[q]);
        for (int i = 1; i < m; i++) {
            q = query[i];
            out.print((q >= maxW) ? " " + maxAnswer : " " + count[q]);
        }

        out.close();
    }

    static class Node {
        int fa, rank;//
        long num;
        ArrayList<Edge> connections;

        Node(int i) {
            fa = i;
            rank = 1;
            num = 1;
            connections = new ArrayList<>();
        }
    }

    static class Edge {
        int weight;
        int u, v;

        Edge(int u, int v, int w) {
            weight = w;
            this.u = u;
            this.v = v;
        }
    }

    static int find(int x) {
        return (x == nodeList[x].fa) ? x : (nodeList[x].fa = find(nodeList[x].fa));
    }

    static void union(int x, int y) {
        if (nodeList[x].rank <= nodeList[y].rank) {
            nodeList[x].fa = y;
            nodeList[y].num = nodeList[y].num + nodeList[x].num;
        } else {
            nodeList[y].fa = x;
            nodeList[x].num = nodeList[x].num + nodeList[y].num;
        }
        if (nodeList[x].rank == nodeList[y].rank && x != y) {
            nodeList[y].rank++;
        }
    }

    static class Reader {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public Reader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public Reader(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException {
            byte[] buf = new byte[64]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();

            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');

            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            if (din == null)
                return;
            din.close();
        }
    }

}