Edgy Trees

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.

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.

inputFormat

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).

outputFormat

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.

样例

4 4
1 2 1
2 3 1
3 4 1

                                                             252

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