Edgy Trees

题意翻译

给一个无根树,n个顶点,每条边或为红或为黑。 给一个整数k。 对于一个k个顶点的序列,如果它满足下列条件称为good: 我们从a1到ak走一条路径(途经点可以重复) 从a1到a2走的是a1到a2的最短路径,a2到a3……ak-1到ak。 如果走过了至少一个黑边则为good。 输入n和k,下面n-1行包含三个整数ui,vi,xi,表示一条边的两个顶点和它的颜色(0为红,1为黑)。 输出good序列的次数%1000000007。

题目描述

You 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. ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF1139C/fceedad9154dba8252692b9078d5d0099b72c637.png)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 $ .

输入输出格式

输入格式


The 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).

输出格式


Print the number of good sequences modulo $ 10^9 + 7 $ .

输入输出样例

输入样例 #1

4 4
1 2 1
2 3 1
3 4 1

输出样例 #1

252

输入样例 #2

4 6
1 2 0
1 3 0
1 4 0

输出样例 #2

0

输入样例 #3

3 5
1 2 1
2 3 0

输出样例 #3

210

说明

In 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.