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 functools
import os.path

Base = 1000000007

class Dsu:
    par = []
    cnt = []
    def __init__(self,size):
        self.par = [x for x in range(size + 2)]
        self.cnt = [1] * (size + 2)
        
    def findp(self,u):
        if self.par[u] == u:
            return u 
        else :
            self.par[u] = self.findp(self.par[u])
            return self.par[u]
        
    def join(self,u,v):
        u,v = self.findp(u),self.findp(v)
        if u == v :
            return
        if self.cnt[u] < self.cnt[v] :
            u,v = v,u
        self.cnt[u] += self.cnt[v]
        self.par[v] = u
        
    def getSize(self,u):
        return self.cnt[self.findp(u)]

def mulmod(u,v):
    return ((u % Base) * (v % Base)) % Base

def submod(u,v):
    return ((u % Base) - (v % Base) + Base) % Base

def fastExp(x,h):
    ret = 1
    while h > 0:
        if h & 1 == 1 :
            ret = mulmod(ret,x)
        x = mulmod(x,x)
        h = h // 2
    return ret

def solve():
    # code goes here!!         
    n,k = map(int,input().split())
    dsu = Dsu(n)
    for i in range(1,n):
        u,v,x = map(int,input().split())
        if x == 0:
            dsu.join(u,v)
            
    ans = functools.reduce(lambda x,y : x - y,map(lambda u : fastExp(dsu.getSize(u),k),filter(lambda u : dsu.findp(u) == u,range(1,n + 1))),fastExp(n,k))
    print(ans)
    

def main():
    # comment when submit.
    if os.path.exists('test.inp') :
        sys.stdin = open("test.inp","r")
    solve()

if __name__ == '__main__':
    main()


