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

class Node():
    def __init__(self):
        self.data=0
        self.parent=None
        self.rank=0

d={}
def makeSet(data):
    node=Node()
    node.data=data
    node.parent=node
    d[data]=node

def get(val):
    return (val*(val-1))//2

def union(data1,data2,ele,res):
    node1=d[data1]
    node2=d[data2]
    parent1=find(node1)
    parent2=find(node2)

    temp=res
    
    temp-=get(ele[parent1.data])
    temp-=get(ele[parent2.data])
    if(parent1.rank>=parent2.rank):
        parent1.rank=(parent1.rank+1 if(parent1.rank==parent2.rank) else parent1.rank)
        parent2.parent=parent1
        ele[parent1.data]+=ele[parent2.data]
    else:
        parent1.parent=parent2
        ele[parent2.data]+=ele[parent1.data]
    
    temp+=get(ele[parent1.parent.data])
    
    return temp

def findData(data):
    return find(d[data]).data


def find(node):
    parent=node.parent
    if(parent==node):
        return node
    node.parent=find(node.parent)
    return node.parent

n,q=map(int,input().split())
ar=[]
for i in range(n-1):
    a,b,w=map(int,input().split())
    ar.append((a,b,w))
qr=[int(x) for x in input().split()]

for i in range(q):
    qr[i]=(qr[i],i)
  
ar.sort(key=lambda x:x[2])
qr.sort(key=lambda x:x[0])

for i in range(1,n+1):
    makeSet(i)
    
ele=[1]*(n+1)
ans=[]
res=0
pos=0
for i in range(q):
    while(pos<n-1 and ar[pos][2]<=qr[i][0]):
        res=union(ar[pos][0],ar[pos][1],ele,res)
        pos+=1
    ans.append((str(res),qr[i][1]))
ans.sort(key=lambda x:x[1])
r=[]
for i in ans:
    r.append(i[0])
print(' '.join(r))