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.Scanner;

public class nextgraph {
	static boolean visited[];
	static ArrayList<Integer> ar[];
	static long mod = (long)1e9 + 7;
	static long count=0l;
	public static void dfs(int i)
	{
		visited[i]=true;
		count++;
		
		for(int x:ar[i])
		{
			if(!visited[x])
			{
				dfs(x);
			}
		}
		
	}static long fast_pow(long a, long b) {
		if(b == 0)
			return 1L;

		long val = fast_pow(a, b / 2);

		if(b % 2 == 0)
			return val * val % mod;
		else 
			return val * val % mod * a % mod;
	}
	public static void main(String args[])
	{
		Scanner scan=new Scanner(System.in);
		int n=scan.nextInt();
		int k=scan.nextInt();
		ar=new ArrayList[n];
		for(int i=0;i<n;i++)ar[i]=new ArrayList<Integer>();
		for(int i=0;i<n-1;i++)
		{
			int u=scan.nextInt()-1;
			int v=scan.nextInt()-1;
			int col=scan.nextInt();
			if(col==0)
			{
				ar[u].add(v);
				ar[v].add(u);
			}
		}
		visited=new boolean[n];
		long tot=fast_pow(n,k);
		long diff=0L;
		for(int i=0;i<n;i++)
		{
			if(!visited[i])
			{
				count=0L;
				dfs(i);
				
				diff+=fast_pow(count,k);
			}
		}
		diff=diff%mod;
		System.out.println((tot-diff+mod)%mod);
	}
}
