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 io, os
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline

from collections import *

def power(a, b, mod):
    res = 1
    
    while b:
        if b%2:
            res = (res*a)%mod
        
        b //= 2
        a = (a*a)%mod    
            
    return res%mod

MOD = 1000000007
n, k = map(int, input().split())
ans = power(n, k, MOD)
adj = defaultdict(list)

for i in range(n-1):
    u, v, x = map(int, input().split())
    if not x:
        adj[u].append(v)
        adj[v].append(u)
        
v = [0]*(1+n)

for i in range(1, 1+n):
    if not v[i]:
        cmp = 0
        q = [i]
        
        while q:
            e = q.pop()
            if not v[e]:
                cmp += 1
            v[e] = 1
            
            for j in adj[e]:
                if not v[j]:
                    q.append(j)

        ans = (ans%MOD-power(cmp, k, MOD))%MOD
                    
print(ans)