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())
par=[-1]*n
def c(x):
  return x*(x-1)//2

def find(x):
  if par[x]<0:
    return x
  else:
    par[x]=find(par[x])
    return par[x]

def unite(x,y):
  x=find(x)
  y=find(y)
  if x==y:
    return False
  else:
    if par[x]>par[y]:
      x,y=y,x
    par[x]+=par[y]
    par[y]=x
    return True

def same(x,y):
  return find(x)==find(y)

def size(x):
  return -par[find(x)]
import collections
Edge=collections.defaultdict(list)
for _ in range(n-1):
  u,v,w=map(int,input().split())
  Edge[w].append((u,v))
Q=[int(i) for i in input().split()]
q=max(Q)
Ans=[0]*(q+1)
ans=0
for i in range(1,q+1):
  for u,v in Edge[i]:
    if same(u-1,v-1):
      continue
    else:
      uu,vv=size(u-1),size(v-1)
      unite(u-1,v-1)
      uv=size(u-1)
      ans+=c(uv)-c(uu)-c(vv)
  Ans[i]=ans
Ans2=[]
for q in Q:
  Ans2.append(Ans[q])
print(*Ans2)