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.
N,K = map(int,raw_input().split())
par = [x for x in range(N)]
rank = [0 for x in range(N)]

def p(a):
    if par[a]==a:
        return a
    return p(par[a])

def join(a,b):
    if rank[a]==rank[b]:
        rank[a] += 1
        par[b] = a
    elif rank[a]<rank[b]:
        par[a] = b
    else:
        par[b] = a

for i in range(N-1):
    a,b,c = map(int,raw_input().split())
    a -= 1
    b -= 1
    if not c:
        a,b = p(a),p(b)
        join(a,b)

arr = [0 for x in range(N)]

mod = pow(10,9)+7

for i in range(N):
    arr[p(i)] += 1

ans = pow(N,K,mod)

for i in range(N):
    cur = pow(arr[i],K,mod)
    ans -= cur
    ans %= mod

print ans


'''
3 2
1 2 1
2 3 1

'''