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
def nc2(val):
    return (val*(val-1)//2)

def find(a,par):
    p=[]
    while(a!=par[a]):
        p.append(a)
        a=par[a]

    for i in p:
        par[i]=a
        
    return a

def union(a,b,par,rank,val,tval):
    if (rank[a]<rank[b]):
        par[a]=b
        val[b]=tval
        
    elif(rank[b]>rank[a]):
        par[b]=a
        val[a]=tval
        
    else:
        par[a]=b
        val[b]=tval
        rank[a]=rank[a]+1

n,m=map(int,input().split())
A=[]
for i in range(n-1):
    u,v,w=map(int,input().split())
    A.append([u,v,w])

A.sort(key=lambda x:x[2])
par=[i for i in range(n+1)]
rank=[0 for i in range(n+1)]
val=[1 for i in range(n+1)]
w=[0 for i in range(2*(10**5)+1)]
tval=0
#print(A)
for i in range(n-1):
    a,b=find(A[i][0],par),find(A[i][1],par)
    #print(a,b,val,par)
    if(a!=b):
        x,y=val[a],val[b]
        tval=tval+(nc2(x+y)-nc2(x)-nc2(y))
        union(a,b,par,rank,val,x+y)
        
    w[A[i][2]]=tval
    #print(tval)
    
v=0
for i in range(2*(10**5)+1):
    if(w[i]!=0):
        v=w[i]
    w[i]=v
    
C=list(map(int,input().split()))
for i in range(m):
    print(w[C[i]],end=" ")
print()