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. 

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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 parser():
    while 1:
        data = list(input().split(' '))
        for number in data:
            if len(number) > 0:
                yield(number)   

input_parser = parser()
def get_word():
    global input_parser
    return next(input_parser)
def get_number():
    data = get_word()
    try:
        return int(data)
    except ValueError:
        return float(data)

def calc(pa,pb,a,b):
    p = max(pa, pb)
    n = min(a,b)
    if pa == pb and n - p > 0:
        #print(a,b, "add", n-p, n, p)
        return n - p
    elif not(pa == pb) and n - p  >= 0:
        #print(a,b, "add D", 1+  n-p, "n :", n, "p:", p)
        return 1 + n - p
    else:
        return 0


class Elem:
    def __init__(self,data):
        self.data = data
        self.parent = self
        self.size = 1

    def merge(self, toElem):
        toParent = toElem.getParent()
        myParent = self.getParent()
        myParent.parent = toParent
        toParent.size += myParent.size
        myParent.size = toParent.size

    def getParent(self):
        if self == self.parent:
            return self
        else:
            return self.parent.getParent()


n = get_number()
k = get_number()

elems = []
for i in range(n):
    elems.append( Elem(i + 1) )
for i in range(n - 1):
        u = get_number()
        v = get_number()
        x = get_number()
        if x == 0:
            elems[u-1].merge(elems[v-1])
groups = []
for i in elems:
    if  i.getParent().data == i.data:
        groups.append([i.data , i.size])


bad = 0
for i in groups:
    bad += i[1]**k
result = n ** k
print(result - bad) 

