B"As you know, an undirected connected graph with n nodes and n xe2 x80 x89- xe2 x80 x891 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: 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 xe2 x80 x89+ xe2 x80 x897). The first line contains two space-separated integers d (0 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89d xe2 x80 x89 xe2 x89 xa4 xe2 x80 x892000) and n (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89n xe2 x80 x89 xe2 x89 xa4 xe2 x80 x892000). The second line contains n space-separated positive integers a1, xe2 x80 x89a2, xe2 x80 x89..., xe2 x80 x89an(1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89ai xe2 x80 x89 xe2 x89 xa4 xe2 x80 x892000). Then the next n xe2 x80 x89- xe2 x80 x891 line each contain pair of integers u and v (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89u, xe2 x80 x89v xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89n) denoting that there is an edge between u and v. It is guaranteed that these edges form a tree. Print the number of valid sets modulo 1000000007. In the first sample, there are exactly 8 valid sets: {1}, xe2 x80 x89{2}, xe2 x80 x89{3}, xe2 x80 x89{4}, xe2 x80 x89{1, xe2 x80 x892}, xe2 x80 x89{1, xe2 x80 x893}, xe2 x80 x89{3, xe2 x80 x894} and {1, xe2 x80 x893, xe2 x80 x894}. Set {1, xe2 x80 x892, xe2 x80 x893, xe2 x80 x894} is not valid, because the third condition isn't satisfied. Set {1, xe2 x80 x894} satisfies the third condition, but conflicts with the second condition."...