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.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Scanner;
import java.io.*;
import java.util.*;

public class Path_Queries {

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] ss = br.readLine().split(" ");
		int n = Integer.parseInt(ss[0]);
		int m = Integer.parseInt(ss[1]);
		int[] par = new int[n];
		int[] size = new int[n];
		int[] x = new int[n-1];
		int[] y = new int[n-1];
		int[] w = new int[n-1];
		Integer[] ind = new Integer[n-1];
		for (int i = 0; i < n; i++) {
			par[i] = i;
			size[i] = 1;
		}
		HashMap<Integer, ArrayList<Integer>> map = new HashMap<>();

		for (int i = 0; i < n - 1; i++) {
			String[] sv = br.readLine().split(" ");
			x[i] = Integer.parseInt(sv[0]) - 1;
			y[i] = Integer.parseInt(sv[1]) - 1;
			w[i] = Integer.parseInt(sv[2]);
			ind[i] = i;
		}

		// Arrays.sort(ind, (u, v) -> w[u] - w[v]);
		Arrays.sort(ind, (e, f) -> w[e] - w[f]);

		HashMap<Integer, Integer> st = new HashMap<>();
		int[] qs = new int[m];
		Integer[] gs = new Integer[m];
		String[] s = br.readLine().split(" ");
		for (int i = 0; i < m; i++) {
			int l = Integer.parseInt(s[i]);
			qs[i] = l;
			gs[i] = i;
		}
		if(n==1){
			System.out.println(0+" "+0);
			return;
		}
		Arrays.sort(gs, (e, f) -> qs[e] - qs[f]);
		int j = 0;
		long ans = 0;
		long[] a = new long[n];
		for (int i = 0; i < gs.length; i++) {
			while (j<n-1&&w[ind[j]] <= qs[gs[i]]) {
				ans += union(x[ind[j]], y[ind[j]], par, size);
				j++;
			}
			a[gs[i]] = ans;
		}
		StringBuilder sb = new StringBuilder();
		for (int i = 0; i < m; i++) {
			sb.append(a[i] + " ");
		}
		System.out.println(sb);
	}

	public static int find(int p, int[] par) {
		if (p == par[p]) {
			return p;
		}
		return par[p] = find(par[p], par);
	}

	public static long union(int a, int b, int[] par, int[] size) {
		int pa = find(a, par);
		int pb = find(b, par);
		long as = size[pa] * 1L * size[pb];
		if (pa != pb) {
			if (pa > pb) {
				par[pb] = pa;
				size[pa] += size[pb];
			} else {
				par[pa] = pb;
				size[pb] += size[pa];
			}
		}
		return as;
	}
}