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 bisect import bisect
from math import inf


def union_init(s):
    d = [i for i in range(s)]
    size = [1 for i in range(s)]
    return (d, size)


def union_query(d, size, n):
    if d[n] != n:
        d[n] = union_query(d, size, d[n])
    return d[n]


def union_merge(d, size, x, y):
    xRoot = union_query(d, size, x)
    yRoot = union_query(d, size, y)

    if xRoot == yRoot:
        return
    if size[xRoot] < size[yRoot]:
        xRoot, yRoot = yRoot, xRoot
    d[yRoot] = xRoot
    size[xRoot] = size[xRoot] + size[yRoot]


def sizeComponent(d, size, x):
    root = union_query(d, size, x)
    return size[root]


nm = input().split()
n = int(nm[0])
m = int(nm[1])

d, size = union_init(n)
pairs = [(0, 0)]
edges = []
for _ in range(n - 1):
    edge = input().split()
    u = int(edge[0]) - 1
    v = int(edge[1]) - 1
    w = int(edge[2])
    edges.append((w, u, v))

edges.sort()
totalP = 0
for e in edges:
    u = e[1]
    v = e[2]
    uSize = sizeComponent(d, size, u)
    vSize = sizeComponent(d, size, v)
    totalP += uSize * vSize
    union_merge(d, size, u, v)
    pairs.append((e[0], totalP))

ms = [int(mi) for mi in input().split()]
answer = [0] * m
for i, mi in enumerate(ms):
    start = bisect(pairs, (mi, inf)) - 1
    answer[i] = pairs[start][1]
print(*answer)