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.PriorityQueue;

public class Main {
    public static int[] fa;
    public static long res;
    public static node[] nodes;
    public static void main(String[] args) throws IOException {
        Reader in=new Reader();
        PrintWriter out=new PrintWriter(System.out);
        int n=in.nextInt();
        int q=in.nextInt();
        fa=new int[n+1];
        nodes=new node[n+1];
        for(int i=1;i<n+1;i++){
            nodes[i]=new node(i);
            fa[i]=i;
        }
        PriorityQueue<edge> edges= new PriorityQueue<>();
        for(int i=0;i<n-1;i++){
            edge temp=new edge(in.nextInt(),in.nextInt(),in.nextInt());
            edges.offer(temp);
        }
        long[][] query=new long[n][2];
        long[] result=new long[q+1];
        long cntLast=0;
        if(!edges.isEmpty()){
            int weightLast=edges.peek().weight;
            int counter=0;
            while (!edges.isEmpty()){
                edge temp=edges.poll();
                int u=find(temp.node1);
                int v=find(temp.node2);
                fa[u]=v;
                long cnt=nodes[u].connected*nodes[v].connected;
                nodes[v].connected+=nodes[u].connected;
                cntLast+=cnt;
                if(temp.weight==weightLast){
                    query[counter][0]=temp.weight;
                    query[counter][1]=cntLast;
                }
                else {
                    counter++;
                    query[counter][0]=temp.weight;
                    query[counter][1]=cntLast;
                }
                weightLast=temp.weight;
            }
            PriorityQueue<Query> queries=new PriorityQueue<>();
            for(int i=1;i<=q;++i){
                queries.offer(new Query(i,in.nextInt()));
            }
            int i=counter;
            while (!queries.isEmpty()){
                Query temp=queries.poll();
                while (i>=0){
                    if(temp.length>=query[i][0]){
                        result[temp.index]=query[i][1];
                        break;
                    }
                    else{
                        i--;
                    }
                }
            }
        }
        for(int j=1;j<=q;j++){
            if(j!=q){
                System.out.print(result[j]+" ");
            }
            else {
                System.out.print(result[j]);
            }
        }
        out.close();
    }
    public static int find(int x){
        if(fa[x]==x) return x;
        return fa[x]=find(fa[x]);
    }
    public static class node{
        long connected;
        int value;
        node(int value){
            this.value=value;
            connected=1;
        }
    }
    static class edge implements Comparable<edge>{
        int weight;
        int node1;
        int node2;
        public edge(int node1,int node2,int weight){
            this.node1=node1;
            this.node2=node2;
            this.weight=weight;
        }
        @Override
        public int compareTo(edge edge) {
            return Integer.compare(weight, edge.weight);
        }
    }
    static class Query implements Comparable<Query>{
        int index;
        int length;
        int negativeLength;
        public Query(int index,int length){
            this.index=index;
            this.length=length;
            this.negativeLength=-length;
        }
        @Override
        public int compareTo(Query query) {
            return Integer.compare(negativeLength, query.negativeLength);
        }
    }
    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();
        }
    }
}