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[] fa;
    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();
        fa=new int[n+1];
        long[] sum=new long[200010];
        for (int i = 0; i <n+1 ; i++) {
            fa[i]=i;
            sum[i]=1;
        }
        int num0,num1,num2;
        Edge[] edges=new Edge[n-1];
        for (int i = 0; i <n-1 ; i++) {
            num0=input.nextInt();
            num1=input.nextInt();
            num2=input.nextInt();
            edges[i]=new Edge(num2,num0,num1);
        }
        Arrays.sort(edges,com1);
        long[] results=new long[200010];

        for (int i = 0; i <n-1 ; i++) {
            num0=find(edges[i].begin);
            num1=find(edges[i].end);
            if(num0==num1){
                continue;
            }
            fa[num0]=num1;
            long num3=sum[num0]*sum[num1];
            sum[num1]+=sum[num0];
            sum[num0]=0;
            results[edges[i].weight]+=num3;
        }
        long currentNum=0;
        for (int i = 0; i <200010 ; i++) {
            if(results[i]!=0){
                currentNum+=results[i];
                results[i]=currentNum;
            }else {
                results[i]=currentNum;
            }
        }
        int index;
        for (int i = 0; i < m; i++) {
            index=input.nextInt();
            out.print(results[index]);
            out.print(" ");
        }


        out.close();
    }

    public static int find(int x) {
        if(fa[x]==x){
            return x;
        }else {
            fa[x]=find(fa[x]);
            return fa[x];
        }
    }

    static class Edge{
        int weight;
        int end;
        int begin;

        public Edge(int weight, int end, int begin) {
            this.weight = weight;
            this.end = end;
            this.begin = begin;
        }
    }
    static Comparator<Edge> com1=new Comparator<Edge>() {
        @Override
        public int compare(Edge o1, Edge o2) {
            return o1.weight-o2.weight;
        }
    };


    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();
        }
    }

}