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:
//Created by Aminul on 10/30/2019.

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

import static java.lang.Math.*;

public class CF1249F {
    static int dp[][][], n, k, a[];
    static ArrayDeque<Integer> g[];

    public static void main(String[] args) throws Exception {
        Scanner in = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        n = in.nextInt();
        k = in.nextInt();
        a = new int[n + 1];
        dp = new int[2][n + 1][n + 2];
        g = genDQ(n + 1);
        ans = 0;
        for (int i = 1; i <= n; i++) {
            a[i] = in.nextInt();
            ans = max(ans, a[i]);
        }
        for (int i = 0; i < n - 1; i++) {
            int u = in.nextInt(), v = in.nextInt();
            g[u].addLast(v);
            g[v].addLast(u);
        }

        dfs(1, 0);
        pw.println(ans);

        pw.close();
    }

    static int ans = 0;
    static void dfs(int u, int p) {
        dp[0][u][0] = a[u];
        dp[1][u][0] = a[u];
        for (int v : g[u]) {
            if (p == v) continue;
            dfs(v, u);
            for (int i = 0; i <= n; i++) {
                for (int j = 0; j <= n; j++) {
                    if(i + j + 1 > k) dp[1][u][min(i, j + 1)] = max(dp[1][u][min(i, j + 1)], dp[0][u][i] + dp[0][v][j]);
                    if(i + j + 1 > k) ans = max(ans, dp[1][u][min(i, j + 1)]);
                }
            }
            for (int i = 1; i <= n + 1; i++) {
                dp[0][u][i] = max(dp[0][u][i], dp[0][v][i - 1]);
                dp[1][u][i] = max(dp[1][u][i], dp[1][v][i - 1]);
                dp[0][u][i] = max(dp[0][u][i], dp[1][u][i]);
            }
            dp[0][u][0] = max(dp[0][u][0], dp[1][u][0]);
        }
        //debug("0", u, dp[0][u]);
        //debug("1", u, dp[1][u]);

    }

    static <T> ArrayDeque<T>[] genDQ(int n) {
        ArrayDeque<T> list[] = new ArrayDeque[n];
        for (int i = 0; i < n; i++) list[i] = new ArrayDeque<T>();
        return list;
    }

    static void debug(Object... obj) {
        System.err.println(Arrays.deepToString(obj));
    }
}