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.util.*;
import java.io.*;

public class G {
    public static void main(String[] args) throws IOException {
        FastScanner input = new FastScanner(System.in);
        // Scanner input = new Scanner(new File("input.txt"));
        PrintWriter output = new PrintWriter(System.out);

        int n = input.nextInt(), m = input.nextInt();
        Edge[] edge = new Edge[n - 1];
        for (int i = 0; i < n - 1; i++) {
            int u = input.nextInt(), v = input.nextInt(), w = input.nextInt();
            edge[i] = new Edge(u - 1, v - 1, w);
        }
        Arrays.sort(edge);

        long[] ans = new long[m];
        Pair[] q = new Pair[m];
        for (int i = 0; i < m; i++) 
            q[i] = new Pair(input.nextInt(), i);

        Arrays.sort(q);

        UnionFind unionFind = new UnionFind(n);

        int index = 0;
        for (Pair pair: q) {
            while (index < edge.length && edge[index].weight <= pair.first) {
                unionFind.union(edge[index].src, edge[index].dest);
                index++;
            }
            ans[pair.second] = unionFind.count;
        }
        for (int i = 0; i < m - 1; i++)
            System.out.print(ans[i] + " ");
 
        System.out.println(ans[m - 1]);

        output.close();
    }
 
    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;
 
        FastScanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }
 
        FastScanner(FileReader s) {
            br = new BufferedReader(s);
        }
 
        String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }
 
        String nextLine() throws IOException {
            return br.readLine();
        }
 
        double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }
 
        int nextInt() throws IOException {
            return Integer.parseInt(next());
        }
 
        long nextLong() throws IOException {
            return Long.parseLong(next());
        }
    }
}

class Pair implements Comparable<Pair> {
    public int first, second;

    public Pair(int first, int second) {
        this.first = first;
        this.second = second;
    }

    public int compareTo(Pair p) {
        return first - p.first;
    }
}

 
class Edge implements Comparable<Edge> {
    public int src, dest, weight;

    public Edge(int src, int dest, int weight) {
        this.src = src;
        this.dest = dest;
        this.weight = weight;
    }

    public int compareTo(Edge e1) {
        return this.weight - e1.weight;
    }

    public String toString() {
        return src + " " + dest + " " + weight;
    }
}

class Subset {
    public int parent;
    public long size;

    public Subset(int parent, int size) {
        this.parent = parent;
        this.size = size;
    }
}

class UnionFind {
    public int V, E;
    public long count = 0;
    public Subset[] subset;

    public UnionFind(int V) {
        this.V = V;

        subset = new Subset[V];
        for (int i = 0; i < V; i++)
            subset[i] = new Subset(i, 1);
    }

    public int getParentOfSubset(int v) {
        if (subset[v].parent == v) return v;
        return subset[v].parent = getParentOfSubset(subset[v].parent);
    }

    public void union(int v, int u) {
        int parentV = getParentOfSubset(v);
        int parentU = getParentOfSubset(u);
        if (parentV == parentU)
            return;

        count = count - subset[parentV].size * (subset[parentV].size - 1) / 2;
        count = count - subset[parentU].size * (subset[parentU].size - 1) / 2;
        long s = subset[parentU].size + subset[parentV].size;
        count = count + s * (s - 1) / 2;

        if (subset[parentV].size < subset[parentU].size) {
            subset[parentV].parent = parentU;
            subset[parentU].size += subset[parentV].size;
        } else {
            subset[parentU].parent = parentV;
            subset[parentV].size += subset[parentU].size;
        }
    }
}