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.

# -*- coding: utf-8 -*-
# @Date    : 2019-03-22 08:08:26
# @Author  : raj lath (oorja.halt@gmail.com)
# @Link    : link
# @Version : 1.0.0

import sys
sys.setrecursionlimit(10**5+1)

inf     =  int(10 ** 20)
max_val =  inf
min_val = -inf

RW  = lambda : sys.stdin.readline().strip()
RI  = lambda : int(RW())
RMI = lambda : [int(x) for x in sys.stdin.readline().strip().split()]
RWI = lambda : [x for x in sys.stdin.readline().strip().split()]

vertices, limit = RMI()
graph = [[] for _ in range(vertices)]
for i in range(vertices - 1):
    u, v, x = RMI()
    graph[u - 1].append((v - 1, x))
    graph[v - 1].append((u - 1, x))
done = [0 for _ in range(vertices)]
comps = []
for i in range(vertices):
    if done[i]:continue
    done[i] = 1
    comps.append([i])
    qu = [i]
    while qu:
        curr_u = qu[0]
        qu = qu[1:]
        for u, x in graph[curr_u]:
            if x == 0 and done[u] == 0:
                qu.append(u)
                done[u] = 1
                comps[-1].append(u)
answer = vertices ** limit

for comp in comps:
    answer -= len(comp) ** limit

print( answer % (10 ** 9 + 7))