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:
n, k = map(int, input().split())
a = list(map(int, input().split()))
g = {}

def dfs(v, p=-1):
	c = [dfs(child, v) for child in g.get(v, set()) - {p}]
	c.sort(key=len, reverse=True)
	r = []
	i = 0
	while c:
		if i >= len(c[-1]):
			c.pop()
		else:
			o = max(i, k - i - 1)
			s = q = 0
			for x in c:
				if len(x) <= o:
					q = max(q, x[i])
				else:
					s += x[o]
					q = max(q, x[i] - x[o])
			r.append(q + s)
			i += 1
	r.append(0)
	for i in range(len(r) - 1, 0, -1):
		r[i - 1] = max(r[i - 1], r[i])
	while len(r) > 1 and r[-2] == 0:
		r.pop()
	o = (r[k] if k < len(r) else 0) + a[v]
	r.insert(0, max(o, r[0]))
	return r


for _ in range(1, n):
	u, v = map(lambda x: int(x) - 1, input().split())
	g.setdefault(u, set()).add(v)
	g.setdefault(v, set()).add(u)

print(dfs(0)[0])