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.
// Java program to print connected components in 
// an undirected graph 
import java.util.Scanner;
import java.util.LinkedList; 
public class Pr3 { 
	// A user define class to represent a graph. 
	// A graph is an array of adjacency lists. 
	// Size of array will be V (number of vertices 
	// in graph) 
	int V; 
	int kk;
	long sum=0;
	int l=0;
	LinkedList<Integer>[] adjListArray; 
	
	// constructor 
	Pr3(int V) { 
		this.V = V; 
		// define the size of array as 
		// number of vertices 
		adjListArray = new LinkedList[V]; 

		// Create a new list for each vertex 
		// such that adjacent nodes can be stored 

		for(int i = 0; i < V ; i++){ 
			adjListArray[i] = new LinkedList<Integer>(); 
		} 
	} 
	
	// Adds an edge to an undirected graph 
	void addEdge( int src, int dest) { 
		// Add an edge from src to dest. 
		adjListArray[src].add(dest); 

		// Since graph is undirected, add an edge from dest 
		// to src also 
		adjListArray[dest].add(src); 
	} 
	
	void DFSUtil(int v, boolean[] visited) { 
		// Mark the current node as visited and print it 
		visited[v] = true; 
		// System.out.print(v+" "); 
		l++;
		// Recur for all the vertices 
		// adjacent to this vertex 
		for (int x : adjListArray[v]) { 
			if(!visited[x]) DFSUtil(x,visited); 
		} 
	} 
	void connectedComponents() { 
		// Mark all the vertices as not visited 
		boolean[] visited = new boolean[V]; 
		for(int v = 0; v < V; ++v) { 
			if(!visited[v]) { 
				// print all reachable vertices 
				// from v 
				DFSUtil(v,visited); 
				// System.out.println("\nNo.: "+l+"\n"); 
				sum+=fast_pow(l,kk,1000000007);
				// System.out.println(sum);
				l=0;

			} 
		} 
	} 

	long fast_pow(long base,long n,long M)
    {
        if(n==0)
           return 1;
        if(n==1)
        return base;
        long halfn=fast_pow(base,n/2,M);
        if(n%2==0)
            return ( halfn * halfn ) % M;
        else
            return ( ( ( halfn * halfn ) % M ) * base ) % M;
    }
	
	
	// Driver program to test above 
	public static void main(String[] args){ 
		// Create a graph given in the above diagram 
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		Pr3 g = new Pr3(n); // 5 vertices numbered from 0 to 4 
		int k=sc.nextInt(),a,b,c,i;
		g.kk=k;
		//Pr3 ob=new Pr3(n);
		for(i=0;i<n-1;i++)
		{
			a=sc.nextInt();
			b=sc.nextInt();
			c=sc.nextInt();
			if(c==0)
				g.addEdge(a-1,b-1);
		}
		//System.out.println("Following are connected components"); 
		g.connectedComponents(); 
		long sum1=(1000000007+g.fast_pow(n,k,1000000007)-g.sum)%1000000007;
		System.out.println(sum1);
	} 
}	 
