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.Arrays;
import java.util.Scanner;

public class QueryPath {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int m = in.nextInt();
        Edge[] Graph = new Edge[n - 1];
        for (int i = 0; i < n - 1; i++) {
            int u = in.nextInt() - 1;
            int v = in.nextInt() - 1;
            int w = in.nextInt();
            Edge x = new Edge(w, u, v);
            Graph[i] = x;
        }
        Arrays.sort(Graph);
        Pair[] query = new Pair[m];
        for (int i = 0; i < m; i++)
            query[i] = new Pair(in.nextInt(), i);
        Arrays.sort(query);
        DSU solver = new DSU(n);
        int l = 0;
        long res = 0;
        for (int i = 0; i < m; i++) {
            while (l < n - 1) {
                if (Graph[l].weight > query[i].first)
                    break;
                int a = Graph[l].from;
                int b = Graph[l].to;
                long szA = solver.getSize(a);
                long szB = solver.getSize(b);
                res -= ((szA * (szA - 1)) / 2) + ((szB * (szB - 1)) / 2);
                solver.unite(a, b);
                szA = solver.getSize(a);
                res += (szA * (szA - 1)) / 2;
                l++;
            }
            query[i].first = res;
            query[i].swap();
        }
        Arrays.sort(query);
        for (int i = 0; i < m; i++)
            System.out.print(query[i].second + " ");
    }
}

class Pair implements Comparable<Pair> {
    long first;
    long second;

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

    public void swap() {
        long tmp = this.first;
        this.first = this.second;
        this.second = tmp;
    }

    @Override
    public int compareTo(Pair arg) {
        if (this.first < arg.first)
            return -1;
        if (this.first == arg.first)
            return 0;
        return 1;
    }
}

class Edge implements Comparable<Edge> {
    long weight;
    int from;
    int to;

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

    @Override
    public int compareTo(Edge arg) {
        if (this.weight < arg.weight)
            return -1;
        if (this.weight == arg.weight)
            return 0;
        return 1;
    }
}

class DSU {
    private int[] parents;
    private long[] size;

    public DSU(int n) {
        parents = new int[n];
        size = new long[n];
        for (int i = 0; i < n; i++) {
            parents[i] = i;
            size[i] = 1;
        }
    }

    public int find(int v) {
        if (v == parents[v])
            return v;
        return parents[v] = find(parents[v]);
    }

    public long getSize(int v) {
        v = find(v);
        return size[v];
    }

    public void unite(int a, int b) {
        a = find(a);
        b = find(b);
        if (a != b) {
            if (size[a] < size[b]) {
                int tmp = a;
                a = b;
                b = tmp;
            }
            parents[b] = a;
            size[a] += size[b];
        }
    }
}