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

public class G {
    static long[] pref;
    static ArrayList<Edge> q;
    static int[] ss;
    public static void main(String[] args) {
        FastScanner scanner = new FastScanner();
        PrintWriter out = new PrintWriter(System.out);
        int n = scanner.nextInt();
        int m = scanner.nextInt();
        PriorityQueue<Edge> queue =new PriorityQueue<>();
        for(int i = 1; i < n; i++) {
            int u = scanner.nextInt()-1, v = scanner.nextInt()-1;
            int w = scanner.nextInt();
            queue.offer(new Edge(u, w, v));
        }
        ss = new int[n];
        pref = new long[m+1];
        q = new ArrayList<>();
        for(int i = 0; i < m; i++) q.add(new Edge(i,scanner.nextInt(), 0));
        Collections.sort(q);
        DSU dsu = new DSU(n);
        while(!queue.isEmpty()) {
            Edge cur = queue.poll();
            int szl = dsu.rank[dsu.find(cur.from)];
            int szr = dsu.rank[dsu.find(cur.to)];
            dsu.union(cur.from, cur.to);
            int ind = Collections.binarySearch(q, new Edge(-1, cur.w,-1));
            if (ind < 0) ind = -ind -1;
            pref[ind] += ((long)szl * szr);
        }
        long[] ans = new long[m];
        for(int i =0; i < m; i++) {
            pref[i+1] += pref[i];
        }
        for(int i = 0; i <m; i++) {
            ans[q.get(i).to] = pref[i];
        }
        for(int i= 0; i < m; i++) {
            out.print(ans[i] + " ");
        }
        out.println();
        out.flush();
    }
    static class DSU {
        int sz;
        int[] parent, rank;
        public DSU(int ss) {
            sz = ss;
            parent = new int[ss];
            rank = new int[ss];
            for(int i = 0; i < ss; i++) {
                rank[i] = 1;
                parent[i] = i;
            }
        }
        int find(int a) {
            int p = a;
            while(parent[a] != a) a = parent[a];
            while(parent[p] != a) {
                int t = parent[p];
                parent[p] = a;
                p = t;
            }
            return a;
        }
        public boolean union(int a, int b) {
            int pa = find(a);
            int pb = find(b);
            if (pa == pb) return false;
            sz--;
            if (rank[pa] <= rank[pb]) {
                rank[pb] += rank[pa];
                parent[pa] = pb;
            } else {
                rank[pa] += rank[pb];
                parent[pb] = pa;
            }
            return true;
        }
    }
    static class Edge implements Comparable<Edge>{
        int to, w, from;
        public Edge(int tt, int ww, int ff) {
            to = tt;
            w = ww;
            from = ff;
        }
        public int compareTo(Edge o) {
            if (w == o.w) return to- o.to;
            return w - o.w;
        }
    }
    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;
        
        public FastScanner(Reader in) {
            br = new BufferedReader(in);
        }
        
        public FastScanner() {
            this(new InputStreamReader(System.in));
        }
        
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        
        int nextInt() {
            return Integer.parseInt(next());
        }
        
        long nextLong() {
            return Long.parseLong(next());
        }
        
        double nextDouble() {
            return Double.parseDouble(next());
        }
        
        String readNextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}