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.io.* ;
import java.math.BigInteger;
import java.util.*;

public class ghh {
	static int count  ;
	static void dfs(int i)
	{
		if(!vis[i])
		{
			vis[i]=true ; count++ ;
			ArrayList<Integer> ve = v.get(i) ; 
			for(int ele: ve) dfs(ele) ;
		}
	}

static ArrayList<ArrayList<Integer>> v ; 
static boolean vis[] ;
	public static void main(String[] args) throws IOException {

		BufferedReader jk = new BufferedReader(new InputStreamReader(System.in)) ;
		PrintWriter out = new PrintWriter(System.out) ;

		StringTokenizer ana = new StringTokenizer(jk.readLine()) ;
		int n = Integer.parseInt(ana.nextToken()) ;
		int k = Integer.parseInt(ana.nextToken()) ;
		vis = new boolean[n] ;
		v= new ArrayList<>() ;
		for(int i=0 ;i<n;i++) v.add(new ArrayList<Integer>()) ;
		for(int i=0 ;i<n-1 ;i++)
		{
			ana = new StringTokenizer(jk.readLine()) ;
			int a = Integer.parseInt(ana.nextToken())-1 ;
			int b = Integer.parseInt(ana.nextToken())-1 ;
			int c = Integer.parseInt(ana.nextToken()) ;
			if(c==0)
			{
				v.get(a).add(b) ; v.get(b).add(a) ;
			}
		}
		BigInteger sum = BigInteger.ZERO ;
		for(int i=0 ;i<n ;i++)
		{
			count =0 ;
			dfs(i) ;
			if(count>0)
			{
				BigInteger d =  new BigInteger(Integer.toString(count)) ;
				d=d.pow(k) ;
		
				sum=sum.add(d) ;
			}
		}
		BigInteger e = new BigInteger(Integer.toString(n)) ;
		e=e.pow(k) ;
		e=e.subtract(sum) ;
		BigInteger big= new BigInteger("1000000007") ;
		e=e.mod(big) ;
		out.println(e);
		

        

		out.flush();
	}

}

