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.io.*;
public class A
{
      public static void main(String ar[]) throws Exception
      {
            BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
            String s1[]=br.readLine().split(" ");
            int n=Integer.parseInt(s1[0]);
            int k=Integer.parseInt(s1[1]);
            HashSet<Integer> hs[]=new HashSet[n+1];
            HashSet<Integer> h=new HashSet<Integer>();
            ArrayList<Integer> al=new ArrayList<Integer>();
            for(int i=1;i<=n;i++)
             hs[i]=new HashSet<Integer>();
            for(int i=0;i<n-1;i++)
            {
              String s2[]=br.readLine().split(" ");
              int x=Integer.parseInt(s2[0]);
              int y=Integer.parseInt(s2[1]);
              int l=Integer.parseInt(s2[2]);
              if(l==0)
              { hs[x].add(y);  hs[y].add(x);  }
            }
            
            for(int i=1;i<=n;i++)
            {
                  //System.out.println(hs[i]);
                  if(h.contains(i))
                   continue;
                  Stack<Integer> st=new Stack<Integer>();
                  st.push(i);
                  int n1=h.size();
                  h.add(i);
                  while(!st.empty())
                  {
                     int x=st.pop();
                     Iterator it=hs[x].iterator();
                     while(it.hasNext())
                     {  
                        int u=(int)it.next(); 
                        if(!h.contains(u))
                        { h.add(u); st.push(u); }
                     }
                  }
                  int n2=h.size();
                 // System.out.println(i+" "+(n2-n1));
                  al.add(n2-n1);
            }
            
           long mod=1000000007;
           long r=1;
           for(int i=0;i<k;i++)
           { r=r*((long)n); r=r%mod; }
           
           long S=0;
           for(int i=0;i<al.size();i++)
           {
               long p=1;
               for(int j=0;j<k;j++)
               { p=p*((long)al.get(i));  p=p%mod; }
               S=(S+p)%mod;
               //System.out.println(al.get(i));
           }
           
           System.out.println((r+mod-S)%mod);
      }
}