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 PYTHON3):

Solution:
from collections import Counter

def find(p, parent):
    if p==parent[p]:
        return p
    parent[p] = find(parent[p], parent)
    return parent[p]

def calc(i):
    return (i*(i-1))//2

def union(x, y, parent, rank, size):
    u = find(x, parent)
    v = find(y, parent)
    if(u==v):
        return 0
    if rank[u]>rank[v]:
        u,v = v,u
    parent[u]=v
    size[v]+= size[u]
    if rank[u]==rank[v]:
        rank[v]+=1
    return size[v]

def count(i, parent, size):
    return size[find(i, parent)]

def solve():
    n,m = map(int, input().split())
    e = []
    parent = {i:i for i in range(1,n+1)}
    rank   = {i:0 for i in range(1,n+1)}
    size   = {i:1 for i in range(1,n+1)}
    for _ in range(n-1):
        x, y, w = map(int, input().split())
        e.append((w, (x,y)))

    e.sort()
    l = list(map(int, input().split()))
    a = [i for i in l]
    a.sort()
    j=0
    ans = {}
    x = 0
    for i in a:
        while j<n-1 and e[j][0]<=i:
            u = count(e[j][1][0], parent, size)
            v = count(e[j][1][1], parent, size)
            w = union(e[j][1][0], e[j][1][1], parent, rank, size)
            j+=1
            x += calc(w)-calc(u)-calc(v)
        ans[i]=x
    z = []
    for i in l:
        z.append(ans[i])
    print(*z)
        

solve()