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.*;

import javax.print.attribute.standard.Finishings;
 
public class Main {
	static int[] p, rank, setSize;
	static int numSets,N;

	public static int findSet(int i) { return p[i] == i ? i : (p[i] = findSet(p[i])); }

	public static boolean isSameSet(int i, int j) { return findSet(i) == findSet(j); }

	public static void unionSet(int i, int j) 
	{ 
		if (isSameSet(i, j)) 
			return;
		numSets--; 
		int x = findSet(i), y = findSet(j);
		if(rank[x] > rank[y]) { p[y] = x; setSize[x] += setSize[y]; }
		else
		{	p[x] = y; setSize[y] += setSize[x];
			if(rank[x] == rank[y]) rank[y]++; 
		} 
	}
	static class edge implements Comparable<edge>{
		int u;int v;int cost;
		edge(int x,int y,int z){
			u=x;v=y;cost=z;
		}
		@Override
		public int compareTo(edge o) {
			// TODO Auto-generated method stub
			return cost-o.cost;
		}
		
	}
	public static void main(String[] args) throws IOException {
		MScanner sc=new MScanner(System.in);
		PrintWriter pw=new PrintWriter(System.out);
		N=sc.nextInt();int m=sc.nextInt();
		p = new int[numSets = N];
		rank = new int[N];
		setSize = new int[N];
		for (int i = 0; i < N; i++) {  p[i] = i; setSize[i] = 1; }
		edge[]in=new edge[N-1];
		for(int i=0;i<N-1;i++) {
			in[i]=new edge(sc.nextInt()-1,sc.nextInt()-1,sc.nextInt());
		}
		Arrays.sort(in);
		long[]ans=new long[(int)2e5+1];
		for(int i=0;i<N-1;i++) {
			edge cur=in[i];
			long size1=setSize[findSet(cur.u)];
			long size2=setSize[findSet(cur.v)];
			ans[cur.cost]+=size1*size2;
			//System.out.println(cur.cost+" "+size1+" "+size2);
			unionSet(cur.u, cur.v);
		}
		for(int i=1;i<ans.length;i++) {
			ans[i]+=ans[i-1];
		}
		for(int i=0;i<m;i++) {
			pw.print(ans[sc.nextInt()]+" ");
		}
		pw.flush();
	}
    static class MScanner {
		StringTokenizer st;
		BufferedReader br;
 
		public MScanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}
 
		public MScanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}
 
		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
 
		public String nextLine() throws IOException {
			return br.readLine();
		}
 
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
 
		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}
 
		public char nextChar() throws IOException {
			return next().charAt(0);
		}
 
		public Long nextLong() throws IOException {
			return Long.parseLong(next());
		}
 
		public boolean ready() throws IOException {
			return br.ready();
		}
 
		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
}