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, m = map(int, input().split())
maxN = 2 * (10 ** 5) + 10
edges = [[] for i in range(0, maxN)]
que = [[] for _ in range(0, maxN)]
ans = [0] * m
sz = [1 for _ in range(0, n)]
p = [i for i in range(0, n)]
total_sum = 0

def get(u):
    if p[u] == u:
        return u
    p[u] = get(p[u])
    return p[u]


def unite(u, v):
    u = get(u)
    v = get(v)
    if u == v:
        return
    global total_sum
    total_sum -= (sz[u] * (sz[u] - 1)) // 2
    total_sum -= (sz[v] * (sz[v] - 1)) // 2
    total_sum += ((sz[u] + sz[v]) * (sz[u] + sz[v] - 1)) // 2
    if sz[u] < sz[v]:
        p[u] = v
        sz[v] += sz[u]
    else:
        p[v] = u
        sz[u] += sz[v]


for i in range(1, n):
    u, v, w = map(int, input().split())
    u -= 1
    v -= 1
    edges[w].append((u, v))
ques = list(map(int, input().split()))

for i in range(0, m):
    que[ques[i]].append(i)
for i in range(0, maxN):
    for u, v in edges[i]:
        unite(u, v)
    for id in que[i]:
        ans[id] = total_sum
print(" ".join(str(x) for x in ans))