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 class Task {

        public void solve(Reader in, PrintWriter out) throws IOException {
            DSU d = new DSU();
            long[] ans = new long[114514*2];
            int n = in.nextInt();
            int m = in.nextInt();
            d.init(n);
            for(int i=1;i<n;i++){
                d.a[i] = new DSU.Node(in.nextInt(),in.nextInt(),in.nextInt());
            }
            Arrays.sort(d.a,1,n);


            for(int i=1;i<n;i++){
                ans[d.a[i].v] += (long) d.he[d.find(d.a[i].x)] *d.he[d.find(d.a[i].y)];
                d.merge(d.a[i].x,d.a[i].y);
            }

            for(int i=1;i<n+2;i++){
                ans[i]+=ans[i-1];
            }
            while (m-->0){
                out.print(ans[in.nextInt()]+" ");
            }

        }

        static class DSU{
            final int N = 114514*2;
            int[] father, he;
            Node[] a;
            public DSU(){
                father = new int[N];
                he = new int[N];
                a = new Node[N];
            }

            void init(int n){
                for(int i=0;i<=n;i++){
                    father[i]=i;
                    he[i]=1;
                }
            }

            static class Node implements Comparable{
                int x,y;
                int v;
                public Node(int x, int y, int v){
                    this.x=x;
                    this.y=y;
                    this.v=v;
                }

                @Override
                public int compareTo(Object o) {
                    Node oo = (Node) o;
                    return this.v-oo.v;
                }
            }


            int find(int x){
//                System.out.println("find "+x);
                if(x==father[x]){
                    return x;
                }
                return father[x]=find(father[x]);
            }
            void merge(int x,int y){
                x=find(x);
                y=find(y);
                father[y]=x;
                he[x]+=he[y];
            }

        }
    }


    public static void main(String[] args) throws IOException {
        Reader in=new Reader();
        PrintWriter out=new PrintWriter(System.out);
        Task solver = new Task();
        solver.solve(in, out);
        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();
        }
    }

}