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())
edges = [list(map(int, input().split())) for i in range(n - 1)]
queries = list(map(int, input().split()))
edges.sort(key = lambda x: x[2])

p = [i for i in range(n+1)]
sz = [1] * (n+1)
r = [1] * (n+1)

ans = [0] * (200005)

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

def join(u, v):
      u = get(u)
      v = get(v)
      if u != v:
            if r[u] < r[v]:
                  u, v = v, u
            if r[u] == r[v]:
                  r[u] = r[u] + 1
            p[v] = u
            temp = sz[u] * sz[v]
            sz[u] += sz[v]
            return temp
      return 0

for e in edges:
      ans[e[2]] += join(e[0], e[1]) 

for i in range(1, 200005):
      ans[i] += ans[i-1];

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