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 a_{i} associated with it.

We call a set S of tree nodes valid if following conditions are satisfied: S is non-empty. 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. $\operatorname{max}_{u \in S} a_{u} - \operatorname{min}_{v \in S} a_{v} \leq d$.

Your task is to count the number of valid sets. Since the result can be very large, you must print its remainder modulo 1000000007 (10^9 + 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 a_1, a_2, ..., a_{n}(1 ≤ a_{i} ≤ 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.