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 sys
input = sys.stdin.readline

n,m = map(int,input().split())
edges = []

for _ in range(n-1):
    i,j,w = map(int,input().split())
    edges.append((i-1,j-1,w))

edges.sort(key = lambda e:e[-1])

Q = list(map(int,input().split()))
ans = [-1]*m

I = sorted(list(range(m)), key = lambda i:Q[i])

UF = [x for x in range(n)]
sz = [1]*n

def find(i):
    if UF[i] != i:
        UF[i] = find(UF[i])
    return UF[i]

cur = 0
def union(i,j):
    global cur
    pi = find(i)
    pj = find(j)
    x = sz[pi]
    y = sz[pj]
    
    cur -= x*(x-1)//2 + y*(y-1)//2
    cur += (x+y)*(x+y-1)//2

    if x >= y:
        sz[pi] += sz[pj]
        UF[pj] = pi
    else:
        sz[pj] += sz[pi]
        UF[pi] = pj

k = 0
for idx in I:
    while k < n-1 and edges[k][-1] <= Q[idx]:
        i,j,w = edges[k]
        k += 1
        union(i,j)
    ans[idx] = cur
print(*ans)