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.BufferedReader;
import java.io.InputStreamReader;
import java.util.*;
public class CF {

    public static int findParent(int idx, int parent[]){
        if(parent[idx] == idx){
            return idx;
        }
        parent[idx] = findParent(parent[idx], parent);
        return parent[idx];
    }

    public static long merge(int start, int end, int parent[], int rank[]){
        int repA = findParent(start, parent);
        int repB = findParent(end, parent);

        if(repA == repB){
            return 0;
        }

        long difference = (rank[repA] + rank[repB])*1L*(rank[repA] + rank[repB] - 1) -
                rank[repA]*1L*(rank[repA] - 1) - rank[repB]*1L*(rank[repB] - 1);

        if(rank[repA] < rank[repB]){
            parent[repA] = repB;
            rank[repB] += rank[repA];
        } else {
            parent[repB] = repA;
            rank[repA] += rank[repB];
        }

        return difference;
    }


    public static void main(String[] args) throws Exception {

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        StringTokenizer st = new StringTokenizer(br.readLine());
        int n = Integer.parseInt(st.nextToken());
        int m = Integer.parseInt(st.nextToken());

        int rank[] = new int[n + 1];
        int parent[] = new int[n + 1];

        for(int i = 1;i <= n;i++){
            rank[i] = 1;
            parent[i] = i;
        }

        PriorityQueue<Node>pq = new PriorityQueue<Node>();

        for(int i = 1;i < n;i++){
            st = new StringTokenizer(br.readLine());
            int u = Integer.parseInt(st.nextToken());
            int v = Integer.parseInt(st.nextToken());
            int w = Integer.parseInt(st.nextToken());
            pq.add(new Node(u, v, w));
        }

        long pairs[] = new long[200005];

        for(int i = 1;i < pairs.length;i++){
            while(!pq.isEmpty() && i == pq.peek().weight){
                Node currentNode = pq.remove();
                pairs[i] += merge(currentNode.start, currentNode.end, parent, rank);
            }
            pairs[i] += pairs[i - 1];
        }

        st = new StringTokenizer(br.readLine());
        StringBuilder sb = new StringBuilder();

        for(int i = 1;i <= m;i++){
            int num = Integer.parseInt(st.nextToken());
            sb.append(pairs[num] / 2 + " ");
        }

        System.out.println(sb);
    }
}

class Node implements Comparable<Node>{
    int start;
    int end;
    int weight;
    Node(int start, int end, int weight){
        this.start = start;
        this.end = end;
        this.weight = weight;
    }

    @Override
    public int compareTo(Node other){
        return Integer.compare(weight, other.weight);
    }
}