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 sys import stdin, stdout
 
 
class Dsu:
    def __init__(self, n):
        self.dsu = [i for i in range(n + 1)]
        self.sz = [1 for _ in range(n + 1)]
 
    def __get__(self, x):
        if x == self.dsu[x]:
            return x
        self.dsu[x] = self.__get__(self.dsu[x])
        return self.dsu[x]
 
    def join(self, x, y):
        x = self.__get__(x)
        y = self.__get__(y)
        if x == y:
            return 0
        if self.sz[x] < self.sz[y]:
             x, y = y, x
        ret = self.sz[x] * self.sz[y]
        self.sz[x] += self.sz[y]
        self.dsu[y] = x
        return ret
 
 
n, m = map(int, stdin.readline().split())
dsu = Dsu(n)
 
edges = [list(map(int, stdin.readline().split())) for i in range(n - 1)]
queries = [(int(x), i) for i, x in enumerate(stdin.readline().split())]
 
edges.sort(key=lambda x: x[2])
queries.sort(key=lambda x: x[0])
 
index = 0
answer = [0 for i in range(m)]
total = 0
 
for q, i in queries:
    while index < len(edges) and edges[index][2] <= q:
        total += dsu.join(edges[index][0], edges[index][1])
        index += 1
    answer[i] = total
 
for x in answer:
    stdout.write(str(x) + ' ')