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 PathQueries {
    public static void main(String[] args) throws IOException {
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(f.readLine());
        int N = Integer.parseInt(st.nextToken());
        int M = Integer.parseInt(st.nextToken());
        ArrayList<Edge> arr = new ArrayList<>();
        for (int i = 0; i < N-1; i++) {
            st = new StringTokenizer(f.readLine());
            int a = Integer.parseInt(st.nextToken())-1;
            int b = Integer.parseInt(st.nextToken())-1;
            int dist = Integer.parseInt(st.nextToken());
            arr.add(new Edge(a, b, dist));
        }
        Collections.sort(arr, new Comparator<Edge>() {
            @Override
            public int compare(Edge o1, Edge o2) {
                return Integer.compare(o1.dist, o2.dist);
            }
        });
        st = new StringTokenizer(f.readLine());
        ArrayList<Query> quer = new ArrayList<>();
        for (int i = 0; i < M; i++) {
            quer.add(new Query(Integer.parseInt(st.nextToken()), i));
        }
        Collections.sort(quer, new Comparator<Query>() {
            @Override
            public int compare(Query o1, Query o2) {
                return Integer.compare(o1.val, o2.val);
            }
        });
        int cur = 0;
        long[] res = new long[M];
        DisjointSet set = new DisjointSet(N);
        for (Query q : quer) {
            while (cur < N-1 && arr.get(cur).dist <= q.val) {
                set.merge(arr.get(cur).a, arr.get(cur).b);
                cur++;
            }
            res[q.id] = set.sum;
        }
        PrintWriter out = new PrintWriter(System.out);
        for (long val : res) {
            out.println(val);
        }
        out.close();

    }
    static long choose2(long c) {
        if (c < 2) {
            return 0;
        }
        return ((c) * (c-1))/2;
    }
    static class Query {
        int val;
        int id;
        Query(int val, int id) {
            this.val = val;
            this.id = id;
        }
    }
    static class Edge {
        int a;
        int b;
        int dist;
        Edge(int a, int b, int dist) {
            this.a = a;
            this.b  = b;
            this.dist = dist;
        }
    }
    static class DisjointSet {
        HashSet<Integer> valid = new HashSet<>();
        long sum = 0;
        int[] par;
        long[] rank;
        DisjointSet(int n) {
            par = new int[n];
            rank = new long[n];
            for (int i = 0; i < n; i++) {
                par[i] = i;
                rank[i] = 1;
            }
        }
        public int find(int x) {
            if (par[x] != x) {
                return (par[x] = find(par[x]));
            }
            return x;
        }
        public void merge(int x, int y) {
            int parX = find(x);
            int parY = find(y);
            if (parX != parY) {
                sum -= choose2(rank[parX]);
                sum -= choose2(rank[parY]);
                if (rank[parX] > rank[parY]) {
                    par[parY] = parX;
                    rank[parX] += rank[parY];
                    sum += choose2(rank[parX]);
                }
                else {
                    par[parX] = parY;
                    rank[parY] += rank[parX];
                    sum += choose2(rank[parY]);
                }
            }
        }
    }
}