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.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.util.Arrays;
import java.util.Comparator;

public class G {
    public static void main(String[] args) throws IOException {
        Reader in = new Reader();
        int n = in.nextInt();
        int m = in.nextInt();
        int[][] edges = new int[n-1][];

        for (int i = 0; i < n - 1; i++) {
            int start = in.nextInt() - 1;
            int end = in.nextInt() - 1;
            int weight = in.nextInt();
            edges[i] = new int[]{start, end, weight};
        }

        int[][] queries = new int[m][];

        for (int i = 0; i < m; i++) {
            queries[i] = new int[] {in.nextInt(), i};
        }

        DisjointSet dsu = new DisjointSet(n);

        Arrays.sort(edges, Comparator.comparingInt((int[] x) -> x[2]));
        Arrays.sort(queries, Comparator.comparingInt((int[] x) -> x[0]));
        long[] ans = new long[m];
        int p = 0;
        long tot = 0;
        for(int[] q : queries) {
            while(p < n-1 && edges[p][2] <= q[0]) {
                int s1 = dsu.c[dsu.root(edges[p][1])];
                int s2 = dsu.c[dsu.root(edges[p][0])];

                tot -= calc(s1);
                tot -= calc(s2);

                dsu.join(edges[p][0], edges[p][1]);
                s1 = dsu.c[dsu.root(edges[p][0])];
                tot += calc(s1);
                p++;
            }
            ans[q[1]] = tot;
        }

        for(long v: ans) {
            System.out.print(v + " ");
        }
        System.out.println();
    }

    static long calc(int x) {
        return -(long)x * (-(long)(x - 1)) / 2;
    }

    static class DisjointSet{
        int[] c;
        DisjointSet(int n) {
            c = new int[n];
            Arrays.fill(c, -1);
        }

        int root(int u) {
            return c[u] < 0 ? u : (c[u] = root(c[u]));
        }

        void join(int u, int v) {
            int x = root(u);
            int y = root(v);

            if (x != y) {
                if(c[y] < c[x]) {
                    int d = x;
                    x = y;
                    y = d;
                }
                c[x] += c[y];
                c[y] = x;
            }
        }
    }
    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();
        }
    }
}