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 cf582d3;
import java.io.*;
import java.util.*;

public class G {
	static ArrayList<LinkedList<Edge>> tree = new ArrayList<LinkedList<Edge>>();
	static long[] a = new long[200001];
	static long[] sz;
	static int[] dsu;
	public static void main(String[] args) {
		MyScanner sc = new MyScanner();
		int n = sc.nextInt(), m = sc.nextInt();
		sz = new long[n];
		dsu = new int[n];
		for(int i = 0; i < n; i++) {
			tree.add(new LinkedList<Edge>());
			sz[i] = 1;
			dsu[i] = i;
		}
		TreeSet<Edge> edges = new TreeSet<Edge>();
		for(int i = 0; i < n - 1; i++)
			edges.add(new Edge(sc.nextInt() - 1, sc.nextInt() - 1, sc.nextInt()));
		while(!edges.isEmpty()) {
			Edge e = edges.pollFirst();
			int u = dsu(e.u), v = dsu(e.v);
			dsu[v] = u;
			a[e.w] += sz[u] * sz[v];
			sz[u] += sz[v];
		}
		for(int i = 1; i <= 200000; i++)
			a[i] += a[i - 1];
		for(int i = 0; i < m; i++)
			out.print(a[sc.nextInt()] + " ");
		out.println();
		out.close();
	}
	static int dsu(int u) {
		return dsu[u] = (u == dsu[u] ? u : dsu(dsu[u]));
	}
	static class Edge implements Comparable<Edge> {
		int u, v, w;
		public Edge(int U, int V, int W) {
			u = U;
			v = V;
			w = W;
		}
		public int compareTo(Edge e) {
			if(e.w == w && e.u == u)
				return v - e.v;
			if(e.w == w)
				return u - e.u;
			return w - e.w;
		}
	}
	public static PrintWriter out  = new PrintWriter(new BufferedOutputStream(System.out));
	public static class MyScanner {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st;
		String next() {
			while (st == null || !st.hasMoreElements())
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		int nextInt() {
			return Integer.parseInt(next());
		}
		long nextLong() {
			return Long.parseLong(next());
		}
		double nextDouble() {
			return Double.parseDouble(next());
		}
		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}
}