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
import math
def getAndParseInt(num=1):
    string = (sys.stdin.readline()).strip()
    if num==1:
        return int(string)
    else:
        return [int(part) for part in string.split()]

def getAndParseString(num=1,delim=" "):
    string = (sys.stdin.readline()).strip()
    if num==1:
        return string
    else:
        return [part for part in string.split(delim)]

n,k = getAndParseInt(2)
adj_list = [[] for i in range(n+1)]

binary_k = []
temp = k
while temp>0:
    binary_k.append(temp%2)
    temp=temp//2


for i in range(n-1):
    u,v,c = getAndParseInt(2)
    if c!=1:
        adj_list[u].append(v)
        adj_list[v].append(u)

marked = [0]*(n+1)
modulo = 1000000007

def powerMod(base):
   maxp = len(binary_k)-1
   index = 0
   val = base % modulo
   ret_val = 1
   while index<=maxp:
       if binary_k[index]:
           ret_val=(ret_val*val) % modulo
       val = (val * val) % modulo
       index+=1
   return ret_val

def dfs(vertex):
    stack = [vertex]
    size = 0
    while stack:
        cur = stack.pop()
        marked[cur]=1
        size+=1
        for child in adj_list[cur]:
            if not marked[child]:
                stack.append(child)
    return size

total = powerMod(n)
for vertex in range(1,n+1):
    if not marked[vertex]:
       count =  dfs(vertex)
       total = (total - powerMod(count))%modulo

print(total)
