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.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;

public class PathQueries {
	static class Edge implements Comparable<Edge> {
		int from, to, cost;

		public Edge(int f, int t, int c) {
			from = f;
			to = t;
			cost = c;
		}

		@Override
		public int compareTo(PathQueries.Edge o) {
			return cost - o.cost;
		}
	}

	static class Point implements Comparable<Point> {
		int x, y;

		public Point(int xx, int yy) {
			x = xx;
			y = yy;
		}

		@Override
		public int compareTo(PathQueries.Point o) {
			return x - o.x;
		}
	}

	static int[] parent, size;

	static int getParent(int x) {
		if (x == parent[x])
			return x;
		return parent[x] = getParent(parent[x]);
	}

	static void merge(int x, int y) {
		int p1 = getParent(x);
		int p2 = getParent(y);
		if (p1 == p2)
			return;

		parent[p1] = p2;
		int s1 = size[p1];
		int s2 = size[p2];
		size[p1] = s1 + s2;
		size[p2] = s1 + s2;
	}

	public static void main(String[] args) {
		InputReader r = new InputReader(System.in);
		int n = r.nextInt();
		int m = r.nextInt();
		Edge[] edges = new Edge[n - 1];
		for (int i = 0; i < n - 1; i++) {
			edges[i] = new Edge(r.nextInt() - 1, r.nextInt() - 1, r.nextInt());
		}
		Arrays.sort(edges);
		Point[] q = new Point[m];
		for (int i = 0; i < m; i++) {
			int weight = r.nextInt();
			q[i] = new Point(weight, i);
		}
		Arrays.sort(q);
		parent = new int[n];
		size = new int[n];
		for (int i = 0; i < parent.length; i++) {
			parent[i] = i;
			size[i] = 1;
		}
		int currIndex = 0;
		long[] sol = new long[q.length];
		long res = 0;
		for (int i = 0; i < q.length; i++) {
			while (currIndex < edges.length && edges[currIndex].cost <= q[i].x) {
				long s1 = size[getParent(edges[currIndex].from)];
				long s2 = size[getParent(edges[currIndex].to)];
				merge(edges[currIndex].from, edges[currIndex].to);
				long a = (s1 * (s1 - 1)) / 2;
				long b = (s2 * (s2 - 1)) / 2;
				res -= a;
				res -= b;
				long ns = s1 + s2;
				res += ((ns * (ns - 1)) / 2);
				currIndex++;
			}
			sol[q[i].y] = res;
		}
		for (long x : sol)
			System.out.println(x);
	}

	static class InputReader {
		private BufferedReader reader;
		private StringTokenizer tokenizer;

		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream));
			tokenizer = null;
		}

		public InputReader(FileReader stream) {
			reader = new BufferedReader(stream);
			tokenizer = null;
		}

		public String nextLine() {
			try {
				return reader.readLine();
			} catch (IOException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
				return null;
			}
		}

		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

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

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

		public double nextDouble() {
			return Double.parseDouble(next());
		}
	}
}