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=[int(x) for x in input().split()]
link=[0]*(n+1)
size=[0]*(n+1)
arr=[0]*m
res=0
for i in range(1,n+1):
    link[i]=i
    size[i]=1
def find(x):
    while x!=link[x]:
        x=link[x]
    return x
def comb(n):
    return n*(n-1)//2
def unite(a,b,res):
    a=find(a)
    b=find(b)
    if size[a]<size[b]:
        a,b=b,a
    res=res-comb(size[a])-comb(size[b])+comb(size[a]+size[b])
    size[a]+=size[b]
    link[b]=a
    return res
edges=[]
ask=[]
for i in range(n-1):
    x,y,z=[int(x) for x in input().split()]
    edges.append((z,x,y))
edges.sort()
x=0
edges.append((10**100,1,1))
ask=sorted(zip([int(x) for x in input().split()],range(m)))
for i in range(m):
    while edges[x][0]<=ask[i][0]:
        res=unite(edges[x][1],edges[x][2],res)
        x+=1
    arr[ask[i][1]]=res
print(*arr)