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.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

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

    static class GPathQueries {
        public void solve(int testNumber, InputReader c, OutputWriter w) {
            HashMap<Integer, Integer> size = new HashMap<>();
            int n = c.readInt(), m = c.readInt();
            p3 edge[] = new p3[n - 1];
            for (int i = 0; i < n - 1; i++) {
                edge[i] = new p3(c.readInt() - 1, c.readInt() - 1, c.readInt());
            }
            for (int i = 0; i < n; i++) {
                size.put(i, 1);
            }

            Arrays.sort(edge);
            UnionFind dsu = new UnionFind(n);
            pair queries[] = new pair[m];
            for (int i = 0; i < m; i++) {
                queries[i] = new pair(c.readInt(), i);
            }
            Arrays.sort(queries);
            int j = 0;
            long res = 0;
            long ans[] = new long[m];
            for (int i = 0; i < m; i++) {
                while (j < n - 1 && edge[j].w <= queries[i].x) {
                    int xroot = dsu.find(edge[j].x), yroot = dsu.find(edge[j].y);
                    res -= nc2(dsu.componentSize(xroot));
                    res -= nc2(dsu.componentSize(yroot));
                    dsu.unify(edge[j].x, edge[j].y);
                    res += nc2(dsu.componentSize(xroot));
                    j++;
                }
                ans[i] = res;
            }

            long seq[] = new long[m];
            for (int i = 0; i < m; i++) {
                seq[queries[i].y] = ans[i];
            }

            w.printLine(seq);
        }

        private long nc2(long n) {
            return (n * (n - 1)) / 2;
        }

        class p3 implements Comparable<p3> {
            int x;
            int y;
            int w;

            public p3(int x, int y, int w) {
                this.x = x;
                this.y = y;
                this.w = w;
            }

            public int compareTo(p3 o) {
                return this.w - o.w;
            }

        }

        class pair implements Comparable<pair> {
            int x;
            int y;

            pair(int x, int y) {
                this.x = x;
                this.y = y;
            }

            public int compareTo(pair o) {
                return this.x - o.x;
            }

        }

    }

    static class UnionFind {
        private int size;
        private int[] sz;
        private int[] id;
        private int numComponents;

        public UnionFind(int size) {

            if (size <= 0) {
                throw new IllegalArgumentException("Size <= 0 is not allowed");
            }

            this.size = numComponents = size;
            sz = new int[size];
            id = new int[size];

            for (int i = 0; i < size; i++) {
                id[i] = i;
                sz[i] = 1;
            }
        }

        public int find(int p) {

            int root = p;
            while (root != id[root]) {
                root = id[root];
            }

            while (p != root) {
                int next = id[p];
                id[p] = root;
                p = next;
            }

            return root;
        }

        public int componentSize(int p) {
            return sz[find(p)];
        }

        public void unify(int p, int q) {

            int root1 = find(p);
            int root2 = find(q);

            if (root1 == root2) {
                return;
            }

            if (sz[root1] < sz[root2]) {
                sz[root2] += sz[root1];
                id[root1] = root2;
            } else {
                sz[root1] += sz[root2];
                id[root2] = root1;
            }
            numComponents--;
        }

    }

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

        public InputReader(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 readInt() {
            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 isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

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

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(long[] array) {
            for (int i = 0; i < array.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(array[i]);
            }
        }

        public void printLine(long[] array) {
            print(array);
            writer.println();
        }

        public void close() {
            writer.close();
        }

    }
}