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.
rem=10**9+7
def dfshelp(root,v):
    e=1
    for child in nei[root]:
        if child!=v:
            p=dfshelp(child,root)%rem
            e=((e%rem)*(p+1))%rem
    if num<=an[root]<=df+num and (dif.get(root,-1)==-1):
        sdf=e
    else:
        sdf=0
    return sdf%rem

df,n=map(int,raw_input().split())
an=[0]+map(int,raw_input().split())
p=max(an)
arr=[[] for i in range(p+2)]
for i in range(1,n+1):
    arr[an[i]].append(i)
nei=[[] for i in range(n+1)]
for i in range(n-1):
    a,b=map(int,raw_input().split())
    nei[a].append(b)
    nei[b].append(a)
ans=0
for j in range(1,max(an)+1):
    dif={}
    for i in arr[j]:
        num=an[i]
        fg=dfshelp(i,-1)
        ans=(ans+fg)%rem
        dif[i]=1

print ans











