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.
from __future__ import division, print_function
def main():
    if False:
        from future_builtins import ascii, filter, hex, map, oct, zip
        range = xrange
    
    
    def readLine():
        a = input()
        return [int(i) for i in a.split(' ')]
    
    def deg(x, y):
        if y == 1:
            return x
        res = deg(x, y // 2)
        res *= res
        res %= md
        if y % 2 == 1:
            res *= x
            res %= md
        return res
    
    def dfs(v):
        used[v] = True
        c = 0
        for _, to in enumerate(g[v]):
            if used[to] == False:
                c += dfs(to)
        return c + 1
    
    
    nm = readLine()
    n, m = nm[0], nm[1]
    g = [[] for _ in range(n + 1)]
    md = 1000000007
    
    for i in range(n - 1):
        s = readLine()
        x, y, t = s[0], s[1], s[2]
        if t == 0:
            g[x].append(y)
            g[y].append(x)
    ans = deg(n, m)
    used = [False for _ in range (n + 1)]
    for i in range(1, n + 1):
        if used[i] == False:
            b = dfs(i)
            ans = ans - deg(b, m)
            if ans < 0:
                ans += md
    print(ans)

import sys
r = 2000000
sys.setrecursionlimit(r)    

import threading
threading.stack_size(2**27)
a = threading.Thread(target=main)
a.start()
a.join()