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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Objects;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Pranay2516
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastReader in = new FastReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        GPathQueries solver = new GPathQueries();
        solver.solve(1, in, out);
        out.close();
    }

    static class GPathQueries {
        public void solve(int testNumber, FastReader in, PrintWriter out) {
            int n = in.nextInt(), m = in.nextInt();
            Pair<Integer, Pair<Integer, Integer>>[] a = new Pair[n - 1];
            Pair<Integer, Integer>[] q = new Pair[m];
            dsu d = new dsu(n);
            for (int i = 0; i < n - 1; ++i) {
                int u = in.nextInt() - 1, v = in.nextInt() - 1, w = in.nextInt();
                a[i] = new Pair<>(w, new Pair<>(u, v));
            }
            for (int i = 0; i < m; ++i) {
                q[i] = new Pair<>(in.nextInt(), i);
            }
            func.sort(a);
            func.sort(q);
            int j = 0;
            long res = 0;
            long[] ans = new long[m];
            for (int i = 0; i < m; ++i) {
                while (j < n - 1 && a[j].x <= q[i].x) {
                    res -= get(d.sz[d.getPar(a[j].y.x)]);
                    res -= get(d.sz[d.getPar(a[j].y.y)]);
                    d.unite(a[j].y.x, a[j].y.y);
                    res += get(d.sz[d.getPar(a[j].y.x)]);
                    j++;
                }
                ans[q[i].y] = res;
            }
            for (long i : ans) {
                out.print(i + " ");
            }
        }

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

    }

    static class Pair<U, V> implements Comparable<Pair<U, V>> {
        public U x;
        public V y;

        public Pair(U x, V y) {
            this.x = x;
            this.y = y;
        }

        public int compareTo(Pair<U, V> o) {
            int value = ((Comparable<U>) x).compareTo(o.x);
            if (value != 0) return value;
            return ((Comparable<V>) y).compareTo(o.y);
        }

        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Pair<?, ?> pair = (Pair<?, ?>) o;
            return x.equals(pair.x) && y.equals(pair.y);
        }

        public int hashCode() {
            return Objects.hash(x, y);
        }

    }

    static class func {
        public static <T extends Comparable<? super T>> void sort(T[] arr) {
            //Taken from @KharYusuf
            int n = arr.length, mid, h, s, l, i, j, k;
            T[] res = arr.clone();
            n--;
            for (s = 1; s <= n; s <<= 1) {
                for (l = 0; l < n; l += (s << 1)) {
                    h = Math.min(l + (s << 1) - 1, n);
                    mid = Math.min(l + s - 1, n);
                    i = l;
                    j = mid + 1;
                    k = l;
                    while (i <= mid && j <= h)
                        res[k++] = arr[i].compareTo(arr[j]) <= 0 ? arr[i++] : arr[j++];
                    while (i <= mid) res[k++] = arr[i++];
                    while (j <= h) res[k++] = arr[j++];
                    for (k = l; k <= h; k++) arr[k] = res[k];
                }
            }
        }

    }

    static class FastReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private FastReader.SpaceCharFilter filter;

        public FastReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) return -1;
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class dsu {
        public int connected;
        public int[] par;
        public int[] sz;

        public dsu(int n) {
            par = new int[n];
            sz = new int[n];
            for (int i = 0; i < n; i++) {
                par[i] = i;
                sz[i] = 1;
            }
            connected = n;
        }

        public int getPar(int k) {
            while (k != par[k]) {
                par[k] = par[par[k]];
                k = par[k];
            }
            return k;
        }

        public void unite(int u, int v) {
            int par1 = getPar(u), par2 = getPar(v);
            if (par1 == par2) return;
            connected--;
            if (sz[par1] > sz[par2]) {
                int tem = par1;
                par1 = par2;
                par2 = tem;
            }
            sz[par2] += sz[par1];
            sz[par1] = 0;
            par[par1] = par[par2];
        }

    }
}