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.

def input_s():
    return raw_input()

def input_i():
    return int(raw_input())

def input_2_i():
    arr = map(int, raw_input().split())
    return arr[0], arr[1]

def input_3_i():
    arr = map(int, raw_input().split())
    return arr[0], arr[1], arr[2]

def input_i_array():
    return map(int, raw_input().split())

def get_presum(n, arr):
    presum = [arr[0]]
    for i in range(1, n):
        presum.append(presum[i - 1] + arr[i])
    return presum

def dfs(graph, pos, vis):
    if pos in vis or pos not in graph:
        return 0

    vis.add(pos)
    nex = graph[pos]
    ans = 1
    for n in nex:
        if n not in vis:
            ans += 1
        dfs(graph, n, vis)

    return ans
    

def calc(n, k, bad_graph):
    mod = 10 ** 9 + 7
    ans = n
    for i in range(k - 1):
        ans *= n
        ans %= mod

    bad_vis = set()
    for i in range(n):
        pos = i + 1
        g_size = dfs(bad_graph, pos, bad_vis)
        if g_size == 0 or g_size == 1:
            continue
        minus_val = g_size
        for j in range(k - 1):
            minus_val *= g_size
            minus_val %= mod
        
        minus_val -= g_size
        ans -= minus_val

    return (ans - n + 2 * mod) % mod

"""
3 5
1 2 1
2 3 0
"""

n, k = input_2_i()
bad_graph = {}
good_graph = {}

for i in range(n - 1):
    l, r, color = input_3_i()
    if l > r:
        l, r = r, l
    if color == 0:
        bad_graph.setdefault(l, []).append(r)
    
print calc(n, k, bad_graph)
