As you know, an undirected connected graph with n nodes and n - 1 edges is called a tree. You are given an integer d and a tree consisting of n nodes. Each node i has a value ai associated with it.

We call a set S of tree nodes valid if following conditions are satisfied:

  1. S is non-empty.
  2. S is connected. In other words, if nodes u and v are in S, then all nodes lying on the simple path between u and v should also be presented in S.
  3. <image>.



Your task is to count the number of valid sets. Since the result can be very large, you must print its remainder modulo 1000000007 (109 + 7).

Input

The first line contains two space-separated integers d (0 ≤ d ≤ 2000) and n (1 ≤ n ≤ 2000).

The second line contains n space-separated positive integers a1, a2, ..., an(1 ≤ ai ≤ 2000).

Then the next n - 1 line each contain pair of integers u and v (1 ≤ u, v ≤ n) denoting that there is an edge between u and v. It is guaranteed that these edges form a tree.

Output

Print the number of valid sets modulo 1000000007.

Examples

Input

1 4
2 1 3 2
1 2
1 3
3 4


Output

8


Input

0 3
1 2 3
1 2
2 3


Output

3


Input

4 8
7 8 7 5 4 6 4 10
1 6
1 2
5 8
1 3
3 5
6 7
3 4


Output

41

Note

In the first sample, there are exactly 8 valid sets: {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {3, 4} and {1, 3, 4}. Set {1, 2, 3, 4} is not valid, because the third condition isn't satisfied. Set {1, 4} satisfies the third condition, but conflicts with the second condition.
from collections import deque

class Graph:
  def __init__(self, n_vertices):
    self.n_vertices = n_vertices
    self.edges = [set() for i in xrange(n_vertices)]
    self.value = [-1] * n_vertices
    self.visit = [False]*n_vertices

  def color(self, i, c):
    if self.value[i] < 0:
      self.uncolored -= 1
      self.value[i] = c

      for neighbor in self.edges[i]:
        color(neighbor, 1-c)

  def set_value(self, i, val):
    self.value[i] = val

  def add_edge(self, i, j):
    self.edges[i].add(j)
    self.edges[j].add(i)

  def mydfs(self, u, lo, hi):
    self.visit[u] = True
    result = 1
    for v in self.edges[u]:
      if A[v] == lo and v<root: continue
      if not self.visit[v] and lo <= A[v] <= hi:
        result *= (self.mydfs(v,lo,hi)+1)
        result %= 10**9+7
    return result

  def dfs(self, start=1):
    stack = [start]
    discovered = [False]*self.n_vertices
    while stack:
      u = stack.pop()
      if not discovered[u]:
        yield u
        discovered[u] = True
        for neighbor in self.edges[u]:
          stack.append(neighbor)

  def bfs(self, start=1):
    stack = deque(start)
    discovered = [False]*self.n_vertices
    while stack:
      u = stack.popleft()
      if not discovered[u]:
        yield u
        discovered[u] = True
        for neighbor in self.edges[u]:
          stack.append(neighbor)

  def orderby(order_type='dfs'):
    if order_type == 'dfs':
      ordering = self.dfs()
    elif order_type == 'bfs':
      ordering = self.bfs()

    rank = [-1]*self.n_vertices
    for i, u in enumerate(ordering):
      rank[u] = i

    return rank

  def reverse_dfs(self, start=1):
    dfs_order = self.orderby(order_type='dfs')

    for u in reversed(list(self.dfs())):
      for child in self.edges[u]:
        if dfs_order[child] > dfs_order[u]:
          self.value[u] += self.value[child]

  def connected_components(self):
    remaining  = set(xrange(self.n_vertices))
    discovered = [False]*self.n_vertices

    while remaining:
      # get arbitrary start element
      start = remaining.pop()

      # initialize component and stack
      component = []
      stack = [start]
      
      while stack:
        u = stack.pop()
        if not discovered[u]:
          component.append(u)
          discovered[u] = True
          for neighbor in self.edges[u]:
            stack.append(neighbor)

      # remove component from remaining
      for v in component:
        if v==start: continue
        else: remaining.remove(v)

      yield component

class Tree:
  def __init__(self, id):
    self.id = id
    self.v = 1
    self.children = []

  def add_child(self, tree):
    self.children.append(tree)

  def prune(self,lo,hi):
    if lo <= A[self.id] <= hi:
      t = Tree(self.id)
      for child in self.children:
        subtree = child.prune(lo,hi)
        if subtree:
          t.children.append(subtree)
      return t
    else:
      return False

  def valid(self):
    for child in self.children:
      self.v *= child.valid() + 1
    return self.v

  def pr(self, depth=0):
    print '%s%d %d'%('\t'*depth, self.id, A[self.id])
    for child in self.children:
      child.pr(depth+1)


d,n = map(int, raw_input().split())
A   = map(int, raw_input().split())
G   = Graph(n)
for i in xrange(n-1):
  u,v = map(int, raw_input().split())
  u,v = u-1,v-1
  G.add_edge(u,v)

total = 0
for i in xrange(n):
  root = i
  total += G.mydfs(i,A[i],A[i]+d)
  G.visit = [False]*n
print total%(10**9+7)

# order = {v:i for i,v in enumerate(G.dfs(0))}
# nodes = [Tree(_) for _ in xrange(n)]
# for v in xrange(n):
#   for u in G.edges[v]:
#     if order[v] < order[u]:
#       nodes[v].add_child(nodes[u])


# nodes[0].pr()
# print 

# total = 0
# for i in xrange(n):
#   x = nodes[i].prune(A[i],A[i]+d)
#   x.pr()
#   print 
#   total += x.valid()
# print total