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.*;
import java.lang.*;
import java.io.*;


 public class Solution
{
      static int mod = 1000000007;
    public static long pow(long x,int n){
         if(n == 0)
             return 1;
        
        if(n == 1)         
            return x%mod;
    
        long k= ((x%mod)*(x%mod))%mod;
        
        if( (n &1) == 0)
         return pow(k,n/2);
        else
          return ((x%mod)*pow(k,n/2)%mod)%mod;
        
     }
  
    public static void findEdgyTrees(List[] adjl, int n,int k){
          OutputStream output = System.out;
        PrintWriter out = new PrintWriter(output);
        long bad = 0;
       boolean[] visited = new boolean[n+1];
       long ver = 0;
       for(int i=1; i<=n; i++)
          if(!visited[i]){
           long temp = DFS(adjl,i,visited);
           if(temp != 0){
            temp++;
            bad= ((bad%mod)+ pow(temp,k))%mod;
            ver+=temp;
           }
         }
          
        long ans = pow(n,k);
        ans-= bad+n-ver;
         out.println(ans);
    
       out.close();
    }
    
    public static int DFS(List[] adjl,int u, boolean[] visited){
        int ver = 0;
          visited[u] = true;
         List<int[]> edges = adjl[u];
            for(int[] edge : edges){ 
            if(!visited[edge[0]]){
              
                if(edge[1] == 1)
                 continue;
                 
                ver++;
                ver+=DFS(adjl,edge[0],visited);
            }
        }
        return ver;
    }
    
	public static void main (String[] args) throws java.lang.Exception
	{
	   InputStreamReader in = new InputStreamReader(System.in);
	   BufferedReader br = new BufferedReader(in); 
	   
	   StringTokenizer st = new StringTokenizer(br.readLine());
	   int n = Integer.parseInt(st.nextToken());
	   int k = Integer.parseInt(st.nextToken());
	   List[] adjl = new LinkedList[n+1];
	   for(int i=0; i<n+1; i++)
	    adjl[i] = new LinkedList<int[]>();
	    
       for(int i=0;i<n-1; i++){
           st = new StringTokenizer(br.readLine());
           int u = Integer.parseInt(st.nextToken());
           int v = Integer.parseInt(st.nextToken());
           int x = Integer.parseInt(st.nextToken());
           addEdge(u,v,x,adjl);
       }
       findEdgyTrees(adjl,n,k);
	}
	
	public static void addEdge(int u, int v, int x,List[] adjl){
	    adjl[u].add(new int[]{v,x});
	    adjl[v].add(new int[]{u,x});
	}
}
