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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Comparator;
import java.util.StringTokenizer;

public class Main {
    static int pointer;
    static Query[] queries;

    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner();
        PrintWriter out = new PrintWriter(System.out);
        int n = sc.nextInt(), m = sc.nextInt();
        Edge[] edges = new Edge[n - 1];
        for (int i = 0; i < n - 1; i++)
            edges[i] = new Edge(sc.nextInt() - 1, sc.nextInt() - 1, sc.nextInt());
        queries = new Query[m];
        for (int i = 0; i < m; i++)
            queries[i] = new Query(i, sc.nextInt());
        UnionFind dsu = new UnionFind(n);
        Arrays.sort(edges);
        Arrays.sort(queries);
        for (Edge edge : edges) dsu.unionSet(edge.u, edge.v, edge.cost);
        for (int i = 1; i < m; i++)
            queries[i].ans += queries[i - 1].ans;
        Arrays.sort(queries, new Comparator<Query>() {
            @Override
            public int compare(Query o1, Query o2) {
                return o1.idx - o2.idx;
            }
        });
        for (Query q : queries)
            out.print(q.ans + " ");
        out.flush();
        out.close();
    }

    static class Edge implements Comparable<Edge> {
        int u, v, cost;

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

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

    static class Query implements Comparable<Query> {
        int idx, q;
        long ans;


        public Query(int idx, int q) {
            this.idx = idx;
            this.q = q;
        }

        @Override
        public int compareTo(Query o) {
            return q - o.q;
        }
    }

    static class UnionFind {
        int[] p, rank, setSize;
        int numSets;

        public UnionFind(int N) {
            p = new int[numSets = N];
            rank = new int[N];
            setSize = new int[N];
            for (int i = 0; i < N; i++) {
                p[i] = i;
                setSize[i] = 1;
            }
        }

        public int findSet(int i) {
            return p[i] == i ? i : (p[i] = findSet(p[i]));
        }

        public boolean isSameSet(int i, int j) {
            return findSet(i) == findSet(j);
        }

        public void unionSet(int i, int j, int cost) {
            if (isSameSet(i, j))
                return;
            numSets--;
            int x = findSet(i), y = findSet(j);
            int a = setSize[x], b = setSize[y];
            if (rank[x] > rank[y]) {
                p[y] = x;
                setSize[x] += setSize[y];
            } else {
                p[x] = y;
                setSize[y] += setSize[x];
                if (rank[x] == rank[y]) rank[y]++;
            }
            while (pointer < queries.length && queries[pointer].q < cost)
                pointer++;
            if (pointer < queries.length) queries[pointer].ans += 1l * a * b;

        }

        public int numDisjointSets() {
            return numSets;
        }

        public int sizeOfSet(int i) {
            return setSize[findSet(i)];
        }
    }

    static class Scanner {
        BufferedReader br;
        StringTokenizer st;

        Scanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

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

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

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

        int[] nextIntArray(int n) throws IOException {
            int[] ans = new int[n];
            for (int i = 0; i < n; i++)
                ans[i] = nextInt();
            return ans;
        }

    }


}