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.*;
import java.io.*;

public class Main {
	public static void main(String args[]) {new Main().run();}

	FastReader in = new FastReader();
	PrintWriter out = new PrintWriter(System.out);
	void run(){
		work();
		out.flush();
	}
	long mod=1000000007;
	long gcd(long a,long b) {
		return b==0?a:gcd(b,a%b);
	}
	int[] weight;
	ArrayList<Integer>[] graph;
	int[][] dp;
	int k;
	void work() {
		int n=in.nextInt();
		k=in.nextInt();
		dp=new int[n][k+1];
		weight=new int[n];
		for(int i=0;i<n;i++)weight[i]=in.nextInt();
		graph=(ArrayList<Integer>[])new ArrayList[n];
		for(int i=0;i<n;i++) {
			graph[i]=new ArrayList<>();
		}
		for(int i=0;i<n-1;i++) {
			int n1=in.nextInt()-1;
			int n2=in.nextInt()-1;
			graph[n1].add(n2);
			graph[n2].add(n1);
		}
		dfs(0,new boolean[n]);
		out.println(dp[0][0]);
	}
	private void dfs(int node, boolean[] vis) {
		vis[node]=true;
		ArrayList<Integer> list=new ArrayList<>();
		for(int nn:graph[node]) {
			if(!vis[nn]) {
				dfs(nn,vis);
				list.add(nn);
			}
		}
		for(int i=0;i<=k;i++) {
			if(i==0) {
				dp[node][0]=weight[node];
				for(int nn:list) {
					dp[node][0]+=dp[nn][k];
				}
			}else{
				int v1=i-1;
				int v2=Math.max(v1,k-1-v1);
				int sum=0;
				int ret=0;
				for(int nn:list) {
					sum+=dp[nn][v2];
				}
				for(int nn:list) {
					sum-=dp[nn][v2];
					sum+=dp[nn][v1];
					ret=Math.max(ret, sum);
					sum+=dp[nn][v2];
					sum-=dp[nn][v1];
				}
				dp[node][i]=ret;
			}
		}
		for(int i=k-1;i>=0;i--) {
			dp[node][i]=Math.max(dp[node][i], dp[node][i+1]);
		}
	}
}



class FastReader
{
	BufferedReader br;
	StringTokenizer st;

	public FastReader()
	{
		br=new BufferedReader(new InputStreamReader(System.in));
	}

	public String next() 
	{
		if(st==null || !st.hasMoreElements())
		{
			try {
				st = new StringTokenizer(br.readLine());
			} catch (IOException e) {
				e.printStackTrace();
			}
		}
		return st.nextToken();
	}

	public int nextInt() 
	{
		return Integer.parseInt(next());
	}

	public long nextLong()
	{
		return Long.parseLong(next());
	}
}