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.
mod = 10**9 + 7

class Graph: 
	def __init__(self,V): 
		self.V = V 
		self.adj = [[] for i in range(V)] 

	def DFSUtil(self, temp, v, visited): 
		visited[v] = True
		temp.append(v) 
		for i in self.adj[v]: 
			if visited[i] == False: 
				temp = self.DFSUtil(temp, i, visited) 
		return temp 

	def addEdge(self, v, w): 
		self.adj[v].append(w) 
		self.adj[w].append(v) 

	def connectedComponents(self): 
		visited = [] 
		cc = [] 
		for i in range(self.V): 
			visited.append(False) 
		for v in range(self.V): 
			if visited[v] == False: 
				temp = [] 
				cc.append(self.DFSUtil(temp, v, visited)) 
		return cc 

n, k = map(int, input().split())
g = Graph(n)
for i in range(n-1):
	a, b, col = map(int, input().split())
	if col == 0:
		g.addEdge(a-1, b-1)
		g.addEdge(b-1, a-1)

cc = g.connectedComponents() 
count = pow(len(cc[0]), k, mod)
for j in range(1, len(cc)):
	count = (count + pow(len(cc[j]), k, mod))%mod

print(pow(n, k, mod)-count)



