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:
'''input
3 3
1 2 1
2 3 2
1 3 2
'''
from sys import stdin
from copy import deepcopy
from collections import deque, defaultdict


def find_parent(n):
	global parent
	node = n
	while parent[node] != node:
		node = parent[node]
	parent[n] = node
	return parent[n]


def combination(num):
	return (num * (num - 1)) // 2

# main starts
n, m = list(map(int, stdin.readline().split()))
graph = defaultdict(list)
edges = []
for _ in range(n - 1):
	edges.append(list(map(int, stdin.readline().split())))

queries = list(map(int, stdin.readline().split()))

edges.sort(key = lambda x:x[2], reverse = True)
parent = dict()
count = dict()
for i in range(1, n + 1):
	parent[i] = i
	count[i] = 1

ans = [0] * (200001)
while len(edges) > 0:
	u, v, w = edges.pop()

	if u > v:
		u, v = v, u

	pv = find_parent(v)
	pu = find_parent(u)
	ans[w] -= (combination(count[pu]) + combination(count[pv]))
	ans[w] += combination(count[pu] + count[pv])
	count[pu] += count[pv]
	count[pv] = 0
	parent[pv] = parent[pu]
		
	# print(u, v, w)
	# print('parent', parent)
	# print('count', count)
	# print(ans)


for i in range(1, len(ans)):
	ans[i] = ans[i - 1] + ans[i]
# print(ans[:10])

for i in queries:
	print(ans[i], end = ' ')