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:
def find(u):
    if parent[u] == u:
        return u

    parent[u] = find(parent[u])
    return parent[u]


def union(a, b):
    u = parent[a]
    v = parent[b]
    p=size[u]
    q=size[v]

    if size[u] > size[v]:
        parent[v] = u
        size[u] += size[v]

    else:
        parent[u] = v
        size[v] += size[u]

    return p*q








n,m=map(int,input().split())
edges=[]
for j in range(n-1):
    u,v,val=map(int,input().split())
    edges.append([val,u,v])

edges.sort()
parent=[i for i in range(n+1)]
size=[1 for i in range(n+1)]
curr=1
val=[0]*(2*10**5+1)
ind=0
while(curr<=2*10**5):
    res=0
    while(ind<n-1 and edges[ind][0]==curr):
        u,v=edges[ind][1],edges[ind][2]

        if find(u)==find(v):
            pass

        else:
            res+=(union(u,v))

        ind+=1

    val[curr]=res+val[curr-1]
    curr+=1

ans=[]
b=list(map(int,input().split()))
for j in b:
    ans.append(val[j])

print(*ans)