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{

    public static void main(String[] args) throws IOException {
        Reader in=new Reader();
        PrintWriter out=new PrintWriter(System.out);
        int n = in.nextInt();
        int m = in.nextInt();
        Edge[] input = new Edge[n-1];
        int[] friend = new int[n+1];
        long[] theNumber = new long[n+1];
        for (int i = 0; i <n-1; i++) {
            input[i] = new Edge();
            input[i].ui = in.nextInt();
            input[i].vi = in.nextInt();
            input[i].wi = in.nextInt();
        }
        long[] Result = new long[200001];
        Arrays.sort(input);
        for (int i = 1; i <=n; i++) {
              friend[i] = i;
              theNumber[i] = 1;
        }
        for(int i=0;i<n-1;i++){
            int x = Link(input[i].vi,friend);
            int y = Link(input[i].ui,friend);
            Result[input[i].wi] = Result[input[i].wi] + theNumber[x] * theNumber[y];
            exChange(friend,theNumber,x,y);
        }
        for (int i = 0; i <Result.length ; i++) {
            if(i==0){
                continue;
            }
            else {
                Result[i] += Result[i-1];
            }
        }
        long[] Answer = new long[m];
        for (int i = 0; i <m ; i++) {
            int search = in .nextInt();
            Answer[i] = Result[search];
        }
        for (int i = 0; i <m ; i++) {
            out.print(Answer[i]+" ");
        }
        out.close();
    }
    static int Link(int a,int[] friend){
        if(friend[a]==a){
            return a;
        }
        else {
            int x = Link(friend[a],friend);
            friend[a] = x;
            return x;
        }
    }
    static void exChange(int[] friend,long[] theNumber,int x,int y){
        friend[y] = x;
        theNumber[x] += theNumber[y];
    }
    static class Edge implements Comparable<Edge>{
        int ui;
        int vi;
        int wi;

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

}