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>();
            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 u=Integer.parseInt(s2[0]);
                  int v=Integer.parseInt(s2[1]);
                  int x=Integer.parseInt(s2[2]);
                  
                  if(x==1)
                   continue;
                  hs[u].add(v);
                  hs[v].add(u);
            }
            
            long S=0;
            long mod=1000000007;
            for(int i=1;i<=n;i++)
            {
                  if(h.contains(i))
                   continue;
                  Queue<Integer> q=new LinkedList<Integer>();
                  q.add(i);
                  long t=1;
                  h.add(i);
                  while(!q.isEmpty())
                  {
                        int u=q.poll();
                        Iterator it=hs[u].iterator();
                        while(it.hasNext())
                        {
                              int v=(int)it.next();
                              if(!h.contains(v))
                              { h.add(v); q.add(v); t++; }
                        }
                  }
                  
                  long p=1;
                  for(int j=0;j<k;j++)
                  {
                      p=(p*t)%mod;
                  }
                  S=(S+p)%mod;
            }
            long r=1;
            for(int i=0;i<k;i++)
             r=(r*n)%mod;
            System.out.println(r-S);
      }
}