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.Arrays;
import java.util.HashSet;
import java.util.Scanner;

public class D {
	
	static int mod = (int)1e9+7;

	public static void main(String[] args)
	{
		Scanner sc = new Scanner(System.in);
		
		int n = sc.nextInt();
		int k = sc.nextInt();
		
		UnionFind uf = new UnionFind(n);
		for(int i=0;i<n-1;i++)
		{
			int u = sc.nextInt()-1;
			int v = sc.nextInt()-1;
			int c = sc.nextInt();
			
			if(c==0)
				uf.unionSet(u, v);
			
		}
		
		HashSet<Integer> ps = new HashSet<Integer>();
		ArrayList<Integer> cc = new ArrayList<Integer>();
		
		for(int i=0;i<n;i++)
			if(!ps.contains(uf.findSet(i)))
			{
				ps.add(uf.findSet(i));
				cc.add(uf.size[uf.findSet(i)]);
			}
		
		
		long tot = exp(n,k);
		for(int s:cc)
		{
			tot = add(tot,-exp(s,k));
		}
		
		System.out.println(tot);
		
	}
	
	static long add(long a,long b)
	{
		return (mod + a+b)%mod;
	}
	
	static long mul(long a,long b)
	{
		return (a*b)%mod;
	}
	
	static long exp(long base,long pow)
	{
		if(pow==0) return 1;
		long half = exp(base,pow/2);
		
		if(pow%2==0) return mul(half,half);
		return mul(half,mul(half,base));
	}
	
	static class UnionFind
	{
		int[] p;
		int[] size;
		
		UnionFind(int n)
		{
			p = new int[n];
			size = new int[n];
			
			for(int i=0;i<n;i++)
				p[i] = i;
			Arrays.fill(size, 1);
			
		}
		
		int findSet(int i)
		{
			return (p[i]==i)?i:(p[i] = findSet(p[i]));
		}
		
		boolean isSameSet(int i,int j)
		{
			return findSet(i)==findSet(j);
		}
		
		void unionSet(int i,int j)
		{
			int x = findSet(i);
			int y = findSet(j);
 
			if(x==y) return;
			if(size[x]>size[y])
			{
				p[y] = x;
				size[x]+=size[y];
			}
			else
			{
				p[x] = y;
				size[y]+=size[x];
			}
				
		}	
	}
	
}

	   	 	 	  		 				 	 		  			  	