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.
mod = (10**9)+7
def power(x,n,mod):
    res = 1
    while n>0:
        if n%2==1:
            res = (res*x)%mod
        x = (x*x)%mod
        n = n//2
    return res

n,k = list(map(int,input().split()))
arr = []
for i in range(n-1):
    v1,v2,co = list(map(int,input().split()))
    if co==0:
        if len(arr)==0:
            arr = [[v1,v2]]
        else:
            flag= 0 
            for i in arr:
                if (v1 in i) or (v2 in i):
                    flag=1
                    i.append(v1)
                    i.append(v2)
            if flag==0:
                arr.append([v1,v2])
    else:
        if len(arr)==0:
            if v1!=v2:
                arr = [[v1],[v2]]
            else:
                arr = [[v1]]
        else:
            flag1 =0
            flag2= 0
            for i in arr:
                if v1 in i:
                    flag1=1
                if v2 in i:
                    flag2=1
            if flag1==0:
                arr.append([v1])
            if flag2==0:
                arr.append([v2])
count = []
for i in range(len(arr)):
    arr[i] = list(set(arr[i]))
    count.append(len(arr[i]))
for i in range(len(count)):
    count[i] = power(count[i],k,mod)
ans = 0
for i in count:
    ans = (ans+i)%mod
print(power(n,k,mod)-ans)
