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.*;

public class edgyTrees {

	static long m = 1000000007;

	public static long pow(int a, int b) {

		if (b == 0)
			return 1;

		return ((a % m) * (pow(a, b - 1) % m)) % m;

	}

	public static long fact(int a) {
		if (a == 0)
			return 0;

		if (a == 1)
			return 1;

		return ((a % m) * (fact(a - 1) % m)) % m;

	}

	public static void main(String[] args) {
		// TODO Auto-generated method stub

		Scanner s = new Scanner(System.in);

		int n = s.nextInt();
		int k = s.nextInt();

		int graph[][] = new int[n][n];
		
		for (int i = 0; i < n - 1; i++) {
			int a = s.nextInt() - 1;
			int b = s.nextInt() - 1;
			int c = s.nextInt();

			if (c == 0)
				c = -1;

			graph[a][b] = graph[b][a] = c;
		}

		System.out.println(trial(n, graph, k));
		
		s.close();

	}

	static void connected(int graph[][], int source, boolean visited[]) {

		if (visited[source])
			return;

		visited[source] = true;

		for (int i = 0; i < graph.length; i++) {

			if (graph[source][i] == -1 && !visited[i])
				connected(graph, i, visited);
		}

	}

	public static long trial(int V, int graph[][], int k) {
		HashSet<Integer> hashset = new HashSet<>();

		ArrayList<ArrayList<Integer>> ans = new ArrayList<>();

		while (hashset.size() != V) {

			for (int i = 0; i < V; i++) {

				if (hashset.contains(i))
					continue;

				boolean visited[] = new boolean[V];

				if (!hashset.contains(i))
					connected(graph, i, visited);
				ArrayList<Integer> temp = new ArrayList<>();
				for (int i1 = 0; i1 < V; i1++) {

					if (visited[i1]) {
						temp.add(i1);
						hashset.add(i1);
				//		System.out.print(i1+" ");
					}

				}
				//System.out.println();
					ans.add(temp);
				break;

			}

		}

		long notAllowed = 0;
			long count=0;
		for (int i = 0; i < ans.size(); i++) {

			//System.out.println("size "+ans.get(i).size());
			if(ans.get(i).size()==1)
				continue;
			notAllowed = (notAllowed + (pow(ans.get(i).size(), k) % m)) % m;
			
		}
		long total = pow(V, k);

		if(total-notAllowed-V<0)
			return 0;
		
		return (total - notAllowed-count)%m;
	}

}
