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, …, 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. 

<image>

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.

Input

The first line contains two integers n and k (2 ≤ n ≤ 10^5, 2 ≤ k ≤ 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 ≤ u_i, v_i ≤ n, x_i ∈ \{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).

Output

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

Examples

Input


4 4
1 2 1
2 3 1
3 4 1


Output


252

Input


4 6
1 2 0
1 3 0
1 4 0


Output


0

Input


3 5
1 2 1
2 3 0


Output


210

Note

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.
import sys
from collections import defaultdict, deque

length = sys.stdin.readline().strip().split(" ")
n, k = map(int, length)

graph = defaultdict(list)
for _ in range(int(n - 1)):
	line = sys.stdin.readline().strip().split(" ")
	if int(line[2]) == 0:
		graph[int(line[0])].append(int(line[1]))
		graph[int(line[1])].append(int(line[0]))
	else:
		if (int(line[0])) not in graph:
			graph[int(line[0])] = []
		if (int(line[1])) not in graph:
			graph[int(line[1])] = []

visited = set()

def bfs(graph, visited):
	queue = deque()
	graph_parts_sizes = []
	for vertex in graph:
		if vertex in visited:
			continue

		prev_size = len(visited)
		queue.append(vertex)
		while len(queue) != 0:
			vertex = queue.popleft()
			visited.add(vertex)
			for neighbour in graph[vertex]:
				if neighbour not in visited:
					queue.append(neighbour)
		graph_parts_sizes.append(len(visited) - prev_size)
	return graph_parts_sizes

parts_size = bfs(graph, visited)
MODULO = int(1e9 + 7)

answer = (n ** k) % MODULO
for size in parts_size:
	answer -= (size ** k) % MODULO
	answer %= MODULO
print(answer % MODULO)