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 PYTHON):

Solution:

visited = [0]*205
dp = [[0]*205 for i in range(205)]
def dfs(node,g):
    sons = []
    for nb in g[node]:
        if not visited[nb]:
            visited[nb] = 1
            dfs(nb,g)
            sons.append(nb)

    dp[node][0] = ws[node-1]
    for s in sons:
        dp[node][0] += dp[s][k]


    ls = len(sons)
    # print node,sons,g[node]
    for i in range(ls):
        for j in range(k+1):
            d2 = max(k-1-j,0)
            maxd = j+1
            if d2+1<maxd and ls>1:
                d2 = j
            tmp = dp[sons[i]][j]
            for s in range(ls):
                if s==i:
                    continue
                tmp += dp[sons[s]][d2]
            dp[node][maxd] = max(dp[node][maxd],tmp)

    for i in range(k)[::-1]:
        dp[node][i] = max(dp[node][i],dp[node][i+1])



n,k = map(int,raw_input().split(" "))
ws = map(int,raw_input().split(" "))
edges = []

def add(dic,k,v):
    if not dic.has_key(k):
        dic[k] = v
    else:
        dic[k] += v

g = {}
for i in range(n-1):
    a,b = map(int,raw_input().split(" "))
    edges.append((a,b))
    add(g,a,[b])
    add(g,b,[a])
root = 1
visited[root] = 1
if g.has_key(root):
    dfs(root,g)
    print dp[root][0]
else:
    print ws[root-1]