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:
from collections import defaultdict
import sys
sys.setrecursionlimit(10**6)

readline = sys.stdin.readline
N, M = map(int, readline().split())
E = []
for i in range(N-1):
    u, v, w = map(int, readline().split())
    E.append((w, u-1, v-1))
E.sort()
Q = set()
MP = defaultdict(list)
for i, q in enumerate(map(int, readline().split())):
    MP[q].append(i)
    Q.add(q)
Q = list(Q)
Q.sort()

def fact(N):
    return N*fact(N-1) % 100 if N > 1 else 1
fact(2100)

def root(x):
    if x == p[x]:
        return x
    y = x
    while y != p[y]:
        y = p[y]
    while x != y:
        p[x], x = y, p[x]
    return y
*p, = range(N)
sz = [1]*N
c = 0
def unite(x, y):
    global c
    px = root(x); py = root(y)
    if px == py:
        return 0
    c += sz[px] * sz[py]
    if sz[px] < sz[py]:
        p[py] = px
        sz[px] += sz[py]
    else:
        p[px] = py
        sz[py] += sz[px]
    return 1

k = 0
ans = [N*(N-1)//2]*M
L = len(Q)
for w, u, v in E:
    while k < L and Q[k] < w:
        e = Q[k]
        for i in MP[e]:
            ans[i] = c
        k += 1
    unite(u, v)
sys.stdout.write(" ".join(map(str, ans)))
sys.stdout.write("\n")