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.*;
import java.util.*;
public class Solution{

    static class Edge{
        int u, v;

        Edge(int u, int v){
            this.u = u;
            this.v = v;
        }
    }

    static int parent[], rank[];
    static long size[];

    private static int findparent(int u){
        if(parent[u] != u)
            parent[u] = findparent(parent[u]);
        return parent[u];
    }

    private static void union(int u, int v){
        int a = findparent(u), b = findparent(v);

        if(a == b)
            return;

        if(rank[a] > rank[b]){
            parent[b] = a;
            size[a] += size[b];
        }
        else if(rank[b] > rank[a]){
            parent[a] = b;
            size[b] += size[a];
        }
        else{
            rank[a]++;
            parent[b] = a;
            size[a] += size[b];
        }
    }

    public static void main(String args[]){
        Scanner sc = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);

        int t = 1;
        while(t-->0){
            int n = sc.nextInt(), q = sc.nextInt();

            TreeMap<Long, ArrayList<Edge>> map = new TreeMap<>();
            for(int i=0; i<n-1; i++){
                int u = sc.nextInt()-1, v = sc.nextInt()-1;
                long wt = sc.nextLong();

                if(!map.containsKey(wt))
                    map.put(wt, new ArrayList<>());

                map.get(wt).add(new Edge(u, v));
            }

            int no = map.size();

            parent = new int[n];
            size = new long[n];
            rank = new int[n];

            for(int i=0; i<n; i++){
                parent[i] = i;
                size[i] = 1;
                rank[i] = 0;
            }

            long edgeWt[] = new long[no], val[] = new long[no];
            int index = 0;

            for(Map.Entry<Long, ArrayList<Edge>> entry: map.entrySet()){
                edgeWt[index] = entry.getKey();

                for(Edge edge: entry.getValue()){
                    int u = edge.u, v = edge.v, a = findparent(u), b = findparent(v);
                    val[index] += size[a] * size[b];
                    union(a, b);
                }

                index++;
            }

            for(int i=1; i<no; i++)
                val[i] += val[i-1];

            while(q-->0){
                long k = sc.nextLong();

                int low = 0, high = no-1;

                while(low <= high){
                    int mid = low + (high - low)/2;

                    if(edgeWt[mid] <= k)
                        low = mid + 1;
                    else
                        high = mid - 1;
                }

                if(high == -1)
                    pw.println(0);
                else
                    pw.print(+val[high]+" ");
            }
        }
        pw.flush();
        pw.close();
    }
}