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.*;

public class Problem_G {
	static class Edge implements Comparable<Edge> {
		int u, v, w;

		Edge(int u, int v, int w) {
			this.u = u;
			this.v = v;
			this.w = w;
		}

		public int compareTo(Edge e) {
			return w - e.w;
		}
	}

	static int[] par;
	static int[] size;

	public static int find(int x) {
		return par[x] == x ? x : (par[x] = find(par[x]));
	}

	public static long union(int x, int y) {
		x = find(x);
		y = find(y);
		long ret = (long) size[x] * size[y];
		par[y] = x;
		size[x] += size[y];
		return ret;
	}

	public static void main(String[] args) {
		InputReader in = new InputReader();
		StringBuilder out = new StringBuilder();

		int N = in.nextInt();
		int M = in.nextInt();
		Edge[] E = new Edge[N - 1];
		for (int i = 0; i < N - 1; i++) {
			int u = in.nextInt() - 1;
			int v = in.nextInt() - 1;
			int w = in.nextInt();
			E[i] = new Edge(u, v, w);
		}
		Arrays.sort(E);
		par = new int[N];
		size = new int[N];
		for (int i = 0; i < N; i++) {
			par[i] = i;
		}
		Arrays.fill(size, 1);
		int now = 0;
		long[] ans = new long[200001];
		for (int i = 1; i < ans.length; i++) {
			ans[i] += ans[i - 1];
			while (now < N - 1 && E[now].w == i) {
				ans[i] += union(E[now].u, E[now].v);
				now++;
			}
		}
		for (int i = 0; i < M; i++) {
			int q = in.nextInt();
			out.append(ans[q]).append(' ');
		}
		out.setCharAt(out.length() - 1, '\n');

		System.out.print(out);
	}

	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer st;

		public InputReader() {
			reader = new BufferedReader(new InputStreamReader(System.in));
		}

		public String next() {
			while (st == null || !st.hasMoreTokens()) {
				st = new StringTokenizer(nextLine());
			}
			return st.nextToken();
		}

		public String nextLine() {
			try {
				return reader.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return null;
		}

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