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:
def find_ancestor(i, father):
    if father[i] == i:
        return i
    father[i] = find_ancestor(father[i], father)
    return father[i]

def connect(i, j, father, n_child):
    i_anc = find_ancestor(i, father)
    j_anc = find_ancestor(j, father)
    if n_child[i_anc] > n_child[j_anc]:
        n_child[i_anc] += n_child[j_anc]
        father[j_anc] = i_anc
    else:
        n_child[j_anc] += n_child[i_anc]
        father[i_anc] = j_anc

n, m = map(int, input().split())
edges = []
father = [i for i in range(n)]
n_child = [1]*n

for i in range(n-1):
    i, j, w = map(int, input().split())
    edges.append((i-1, j-1, w))

edges.sort(key=lambda x: -x[2])
queries = list(map(int, input().split()))

s_queries = sorted(queries)

# final map the index to the query
ans = {}

w_limit = []
ans_cum = 0
for query in s_queries:
    while len(edges) and edges[-1][2] <= query:
        i, j, w = edges[-1]
        edges.pop()
        i_anc = find_ancestor(i, father)
        j_anc = find_ancestor(j, father)
        # it's tree father may not be same
        ans_cum += n_child[i_anc] * n_child[j_anc]
        connect(i, j, father, n_child)
    ans[query] = ans_cum

print(" ".join(list(map(str, [ans[query] for query in queries]))))