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.Set;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.HashMap;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
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 in, OutputWriter out) {
            int n = in.readInt();
            int m = in.readInt();

            List<List<Edge>> edges = new ArrayList<>();
            for (int i = 0; i <= 200000; i++) {
                edges.add(new ArrayList<>());
            }

            for (int i = 0; i < n - 1; i++) {
                int from = in.readInt() - 1;
                int to = in.readInt() - 1;
                int cost = in.readInt();
                edges.get(cost).add(new Edge(from, to));
            }

            int[] q = in.readIntArray(m);
            long[] ans = new long[200001];
            long sum = 0;
            UnionFind uf = new UnionFind(n);
            for (int i = 0; i <= 200000; i++) {
                for (Edge e : edges.get(i)) {
                    long size1 = uf.size(e.from);
                    long size2 = uf.size(e.to);
                    sum -= size1 * (size1 - 1) / 2;
                    sum -= size2 * (size2 - 1) / 2;
                    uf.union(e.from, e.to);
                    sum += (size1 + size2) * (size1 + size2 - 1) / 2;
                }
                ans[i] = sum;
            }

            for (int i = 0; i < m; i++) {
                if (i > 0) out.print(" ");
                out.print(ans[q[i]]);
            }
            out.printLine();
        }

        class Edge {
            int from;
            int to;

            public Edge(int from, int to) {
                this.from = from;
                this.to = to;
            }

        }

    }

    static class UnionFind {
        protected int[] parent;

        public UnionFind(int size) {
            parent = new int[size];
            Arrays.fill(parent, -1);
        }

        public boolean union(int x, int y) {
            x = root(x);
            y = root(y);
            if (x != y) {
                if (parent[y] < parent[x]) {
                    int tmp = y;
                    y = x;
                    x = tmp;
                }
                parent[x] += parent[y];
                parent[y] = x;
                return true;
            }
            return false;
        }

        public int root(int x) {
            return parent[x] < 0 ? x : (parent[x] = root(parent[x]));
        }

        public int size(int x) {
            return -parent[root(x)];
        }

        public List<Set<Integer>> getGroups() {
            int n = parent.length;
            List<Set<Integer>> groups = new ArrayList<>();
            Map<Integer, Integer> map = new HashMap<>();
            for (int i = 0; i < n; i++) {
                int r = root(i);
                if (!map.containsKey(r)) {
                    map.put(r, groups.size());
                    groups.add(new HashSet<>());
                }
                groups.get(map.get(r)).add(i);
            }
            return groups;
        }

        public String toString() {
            return getGroups().toString();
        }

    }

    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(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void printLine() {
            writer.println();
        }

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

        public void print(long i) {
            writer.print(i);
        }

    }

    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[] readIntArray(int size) {
            int[] array = new int[size];
            for (int i = 0; i < size; i++) {
                array[i] = readInt();
            }
            return array;
        }

        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);

        }

    }
}