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.
import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Basics {

    int mod = 1000000007;
    int n; // 2 <= n <= 10^5
    int k; // 2 <= k <= 100
    List<List<Integer>> neighbours = new ArrayList<>();
    boolean[] visted;
    int color;

    public void run() {
        Scanner sc = new Scanner(System.in);
        n = sc.nextInt();
        k = sc.nextInt();
        for (int i = 0; i < n + 1; i++) {
            neighbours.add(new ArrayList<>());
        }
        visted = new boolean[n + 1];

        for (int i = 0; i < n - 1; i++) {
            int x = sc.nextInt();
            int y = sc.nextInt();
            int w = sc.nextInt();
            if (w == 0) {
                neighbours.get(x).add(y);
                neighbours.get(y).add(x);
            }
        }

        int answer = power(n, k);

        for (int i = 1; i <= n; i++) {
            if (!visted[i]) {
                color++;
                int nodeCount = dfs(i);
                answer = (answer - power(nodeCount, k) + mod) % mod;
            }
        }
        System.out.println(answer);
    }

    int dfs(int start) {
        visted[start] = true;
        int count = 0;
        for (int next : neighbours.get(start)) {
            if (!visted[next]) {
                count += dfs(next);
            }
        }
        return count + 1;
    }

    // raw power is okay
    public int power(int n, int k) {
        long answer = 1;
        for (int i = 0; i < k; i++) {
            answer = (answer * n) % mod;
        }
        // safe cast
        return (int) answer;
    }


    public static void main(String[] args) {
        new Basics().run();
    }
}