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 . . 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).
输入描述:
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.
输出描述:
Print the number of valid sets modulo 1000000007.
示例1
输入
1 4<br />2 1 3 2<br />1 2<br />1 3<br />3 4<br />0 3<br />1 2 3<br />1 2<br />2 3<br />4 8<br />7 8 7 5 4 6 4 10<br />1 6<br />1 2<br />5 8<br />1 3<br />3 5<br />6 7<br />3 4<br />
备注:
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.
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