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.lang.reflect.Array;
import java.math.BigInteger;
import java.net.Inet4Address;
import java.util.*;
import java.lang.*;
import java.util.HashMap;
import java.util.PriorityQueue;
public class Solution implements Runnable{
    static class pair implements Comparable
    {
        int f;
        int s;
        pair(int fi,int se)
        {
            f=fi;
            s=se;
        }
        public int compareTo(Object o)//ascending order
        {
            pair pr=(pair)o;
            if(s>pr.s)
                return 1;
            if(s==pr.s)
            {
                if(f>pr.f)
                    return 1;
                else
                    return -1;
            }
            else
                return -1;
        }
        public boolean equals(Object o)
        {
            pair ob=(pair)o;
            if(o!=null)
            {
                if((ob.f==this.f)&&(ob.s==this.s))
                    return true;
            }
            return false;
        }
        public int hashCode()
        {
            return (this.f+" "+this.s).hashCode();
        }
    }
    public class triplet implements Comparable
    {
        int f,t;
        int s;
        triplet(int f,int s,int t)
        {
            this.f=f;
            this.s=s;
            this.t=t;
        }
        public boolean equals(Object o)
        {
            triplet ob=(triplet)o;
            int ff;
            int ss;
            int tt;
            if(o!=null)
            {
                ff=ob.f;
                ss=ob.s;
                tt=ob.t;
                if((ff==this.f)&&(ss==this.s)&&(tt==this.t))
                    return true;
            }
            return false;
        }
        public int hashCode()
        {
            return (this.f+" "+this.s+" "+this.t).hashCode();
        }
        public int compareTo(Object o)//ascending order
        {
            triplet tr=(triplet)o;
            if(t>tr.t)
                return 1;
            else
                return -1;
        }
    }
    void merge1(int arr[], int l, int m, int r)
    {
        int n1 = m - l + 1;
        int n2 = r - m;
        int L[] = new int [n1];
        int R[] = new int [n2];
        for (int i=0; i<n1; ++i)
            L[i] = arr[l + i];
        for (int j=0; j<n2; ++j)
            R[j] = arr[m + 1+ j];
        int i = 0, j = 0;
        int k = l;
        while (i < n1 && j < n2)
        {
            if (L[i]<=R[j])
            {
                arr[k] = L[i];
                i++;
            }
            else
            {
                arr[k] = R[j];
                j++;
            }
            k++;
        }
        while (i < n1)
        {
            arr[k] = L[i];
            i++;
            k++;
        }
        while (j < n2)
        {
            arr[k] = R[j];
            j++;
            k++;
        }
    }
    void sort1(int arr[], int l, int r)
    {
        if (l < r)
        {
            int m = (l+r)/2;
            sort1(arr, l, m);
            sort1(arr , m+1, r);
            merge1(arr, l, m, r);
        }
    }
    int par[],size[],rank[];
    long ans=0;
    HashSet<Integer>hs=new HashSet<>();
    long res(int x)
    {
        long y=x;
        long z=(y*(y-1))/2;
        return z;
    }
    void makeset(int i)
    {
        par[i]=i;
        size[i]=1;
        rank[i]=0;
        hs.add(i);
    }
    int find(int x)
    {
        if(par[x]!=x)
            par[x]=find(par[x]);
        return par[x];
    }
    void union(int a,int b)
    {
        int x=find(a);
        int y=find(b);
        if(x==y)
            return;
        if(rank[x]<rank[y])
        {
            par[x]=y;
            ans-=res(size[x]);
            ans-=res(size[y]);
            ans+=res(size[x]+size[y]);
            size[y]+=size[x];
            hs.remove(x);
        }
        else if(rank[y]<rank[x])
        {
            par[y]=x;
            ans-=res(size[x]);
            ans-=res(size[y]);
            ans+=res(size[x]+size[y]);
            size[x]+=size[y];
            hs.remove(y);
        }
        else
        {
            par[x]=y;
            ans-=res(size[x]);
            ans-=res(size[y]);
            ans+=res(size[x]+size[y]);
            size[y]+=size[x];
            hs.remove(x);
            rank[y]++;
        }
    }
    public static void main(String args[])throws Exception
    {
        new Thread(null,new Solution(),"Solution",1<<27).start();
    }
    public void run()
    {
        try
        {
            InputReader in = new InputReader(System.in);
            PrintWriter out = new PrintWriter(System.out);
            int n=in.ni();
            int m=in.ni();
            PriorityQueue<triplet>pq=new PriorityQueue<>();
            par=new int[n+1];
            size=new int[n+1];
            rank=new int[n+1];
            for(int i=1;i<n;i++)
            {
                int u=in.ni();
                int v=in.ni();
                int x=in.ni();
                pq.add(new triplet(u,v,x));
            }
            for(int i=1;i<=n;i++)
                makeset(i);
            HashMap<Integer,Long>hm=new HashMap<>();
            for(int i=1;i<=200000;i++)
            {
                while(!pq.isEmpty())
                {
                    triplet t=pq.peek();
                    if(t.t>i)
                        break;
                    t=pq.remove();
                    union(t.f,t.s);
                }
                hm.put(i,ans);
            }
            while(m--!=0)
            {
                int x=in.ni();
                out.print(hm.get(x)+" ");
            }
            out.close();
        }
        catch(Exception e){
            return;
        }
    }
    static class InputReader {

        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) {
                curChar = 0;
                try {
                    snumChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int ni() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nl() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int[] nextIntArray(int n) {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = ni();
            }
            return a;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public String nextLine() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

    }
}