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 Main {
    static int[] father;
    static int[] size;
    public static int find(int x) {
        if(x == father[x])
            return x;
        else{
            father[x] = find(father[x]);
            return father[x];
        }
    }
    public static void merge(int i, int j)
    {
        int x = find(i), y = find(j);
        father[y] = x;
        size[x] = size[x] + size[y];
        size[y] = size[x];
    }
    public static void main(String[] args) throws IOException {
        Reader input=new Reader();
        PrintWriter out=new PrintWriter(System.out);
        int n = input.nextInt();
        int m = input.nextInt();
        Edge[] edges = new Edge[n];
        int max = 0;
        for (int i = 1; i < n; i++){
            edges[i] = new Edge();
            edges[i].u = input.nextInt();
            edges[i].v = input.nextInt();
            edges[i].w = input.nextInt();
            if (edges[i].w > max)
                max = edges[i].w;
        }
        int[] queries = new int[m];
        for (int i = 0; i < m; i++){
            queries[i] = input.nextInt();
        }
        Comparator<Edge> comparator = new Comparator<Edge>() {
            @Override
            public int compare(Edge o1, Edge o2) {
                return o1.w - o2.w;
            }
        };
        Arrays.sort(edges, 1, n, comparator);
        father = new int[n + 1];
        size = new int[n + 1];
        for (int i = 1; i <= n; i++){
            father[i] = i;
            size[i] = 1;
        }
        long[] ans = new long[max + 1];
        for (int i = 1; i < n && edges[i].w <= max; i++){
            ans[edges[i].w] = ans[edges[i].w] + (long) size[find(edges[i].u)] * size[find(edges[i].v)];
            merge(edges[i].u, edges[i].v);
        }
        for (int i = 1; i <= max; i++){
            ans[i] = ans[i] + ans[i - 1];
        }
        for (int i = 0; i < m - 1; i++){
            out.printf("%d ", ans[Math.min(queries[i], max)]);
        }
        out.print(ans[Math.min(queries[m - 1], max)]);
        out.close();
    }


    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();
        }
    }
}
class Edge{
    int u;
    int v;
    int w;
}