C. Edgy Treestime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given a tree (a connected undirected graph without cycles) of n vertices. Each of the n - 1 edges of the tree is colored in either black or red.You are also given an integer k. Consider sequences of k vertices. Let's call a sequence [a_1, a_2, \ldots, a_k] good if it satisfies the following criterion:  We will walk a path (possibly visiting same edge/vertex multiple times) on the tree, starting from a_1 and ending at a_k.  Start at a_1, then go to a_2 using the shortest path between a_1 and a_2, then go to a_3 in a similar way, and so on, until you travel the shortest path between a_{k-1} and a_k. If you walked over at least one black edge during this process, then the sequence is good.   Consider the tree on the picture. If k=3 then the following sequences are good: [1, 4, 7], [5, 5, 3] and [2, 3, 7]. The following sequences are not good: [1, 4, 6], [5, 5, 5], [3, 7, 3].There are n^k sequences of vertices, count how many of them are good. Since this number can be quite large, print it modulo 10^9+7.InputThe first line contains two integers n and k (2 \le n \le 10^5, 2 \le k \le 100), the size of the tree and the length of the vertex sequence.Each of the next n - 1 lines contains three integers u_i, v_i and x_i (1 \le u_i, v_i \le n, x_i \in \{0, 1\}), where u_i and v_i denote the endpoints of the corresponding edge and x_i is the color of this edge (0 denotes red edge and 1 denotes black edge).OutputPrint the number of good sequences modulo 10^9 + 7.ExamplesInput
4 4
1 2 1
2 3 1
3 4 1
Output
252Input
4 6
1 2 0
1 3 0
1 4 0
Output
0Input
3 5
1 2 1
2 3 0
Output
210NoteIn the first example, all sequences (4^4) of length 4 except the following are good:   [1, 1, 1, 1] [2, 2, 2, 2] [3, 3, 3, 3] [4, 4, 4, 4] In the second example, all edges are red, hence there aren't any good sequences.
4 4
1 2 1
2 3 1
3 4 1

252
['dfs and similar', 'dsu', 'graphs', 'math', 'trees', '*1500']