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:
// package Quarantine;

import javafx.util.Pair;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class PathQueries {
    public static void build(int size[],int par[],int n){
        for(int i=1;i<=n;i++){
            size[i]=1;
            par[i]=i;
        }
        return;
    }
    public static int findParent(int v,int par[]){
        if(par[v]==v){
            return v;
        }
        int p=findParent(par[v],par);
        par[v]=p;
        return p;
    }
    public static Pair<Integer,Integer> merge(int x, int y, int par[], int size[]){
        int p1=findParent(x,par);
        int p2=findParent(y,par);
        if(p1!=p2){
            if(size[p1]<size[p2]){
                par[p1]=p2;
                size[p2]+=size[p1];
                return new Pair<>(size[p1],size[p2]);
            }
            else{
                par[p2]=p1;
                size[p1]+=size[p2];
                return new Pair<>(size[p2],size[p1]);
            }
        }
        return new Pair<>(0,0);
    }
    public static void main(String[] args)throws IOException {
        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());
        StringBuilder print=new StringBuilder();
        ArrayList<Pair<Integer,Integer>> edges[]=new ArrayList[200001];
        for(int i=1;i<=200000;i++){
            edges[i]=new ArrayList<>();
        }
        int size[]=new int[n+1];
        int par[]=new int[n+1];
        build(size,par,n);
        for(int i=1;i<n;i++){
            st=new StringTokenizer(br.readLine());
            int x=Integer.parseInt(st.nextToken());
            int y=Integer.parseInt(st.nextToken());
            int w=Integer.parseInt(st.nextToken());
            edges[w].add(new Pair<>(x,y));
        }
        long ans[]=new long[200001];
        for(int i=1;i<=200000;i++){
            long prev=ans[i-1];
            for(Pair<Integer,Integer> p:edges[i]){
                int x=p.getKey();
                int y=p.getValue();
                Pair<Integer,Integer> t=merge(x,y,par,size);
//                System.out.println(p.toString()+"p");
//                System.out.println(t.toString());
                int s1=t.getKey();
                int s2=t.getValue();
                s2-=s1;
                if(s1==0&&s2==0){
                    continue;
                }
                if(s1>1){
                    prev-=(1l*s1*(s1-1))/2;
                }
                if(s2>1){
                    prev-=(1l*s2*(s2-1))/2;
                }
                s2+=s1;
                prev+=(1l*s2*(s2-1))/2;
//                System.out.println(prev+"prev");
//                System.out.println(p+" "+i);
            }
            ans[i]=prev;
        }
//        long prefix[]=new long[200001];
//        for(int i=1;i<=200000;i++){
//            prefix[i]=prefix[i-1]+ans[i];
//        }
        st=new StringTokenizer(br.readLine());
        for(int i=1;i<=m;i++){
            int num=Integer.parseInt(st.nextToken());
            print.append(ans[num]+" ");
        }
        System.out.println(print.toString());
    }
}