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:
import heapq
import sys
input = sys.stdin.readline

def get_root(s):
    v = []
    while not s == root[s]:
        v.append(s)
        s = root[s]
    for i in v:
        root[i] = s
    return s

def unite(s, t):
    rs, rt = get_root(s), get_root(t)
    if not rs ^ rt:
        return
    if rank[s] == rank[t]:
        rank[rs] += 1
    if rank[s] >= rank[t]:
        root[rt] = rs
        size[rs] += size[rt]
    else:
        root[rs] = rt
        size[rt] += size[rs]
    return

def get_size(s):
    return size[get_root(s)]

def same(s, t):
    return True if get_root(s) == get_root(t) else False

n, m = map(int, input().split())
h = []
for _ in range(n - 1):
    u, v, w = map(int, input().split())
    heapq.heappush(h, (w, u, v))
heapq.heappush(h, (1145141919, 810, 810))
q = list(map(int, input().split()))
p = []
for i in range(m):
    heapq.heappush(p, (q[i], i))
root = [i for i in range(n + 1)]
rank = [1 for _ in range(n + 1)]
size = [1 for _ in range(n + 1)]
ans = [0] * m
now = 0
while p:
    qi, i = heapq.heappop(p)
    while h[0][0] <= qi:
        w, u, v = heapq.heappop(h)
        su, sv = get_size(u), get_size(v)
        now -= su * (su - 1) // 2
        now -= sv * (sv - 1) // 2
        now += (su + sv) * (su + sv - 1) // 2
        unite(u, v)
    ans[i] = now
print(*ans)