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.HashMap;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		
	Scanner scn = new Scanner(System.in);
    int n = scn.nextInt();
    int k = scn.nextInt();
    ArrayList<HashMap<Integer,Integer>> map = new ArrayList<>();
    for( int i=0;i<n-1;++i){
        int u = scn.nextInt();
        int v = scn.nextInt();
        int c = scn.nextInt();

        if(c==1)
           continue;
        int posu = -1;
        int posv = -1;
        int count =0;
        for(HashMap<Integer,Integer> temp : map){
            if(temp.containsKey(u)){
                posu = count; 
                break;
            }
            count++;
        }
        count = 0;
        for(HashMap<Integer,Integer> temp : map){
            if(temp.containsKey(v)){
                posv = count; 
                break;
            }
            count++;
        }

        if(posu==-1){
            if(posv==-1){
                HashMap<Integer,Integer> dummy = new HashMap<>();
                dummy.put(u,0);
                dummy.put(v,0);
                map.add(dummy);
            }else{
                HashMap<Integer,Integer> dummy = map.get(posv);
                dummy.put(u,0);
            }
        }else{
            HashMap<Integer,Integer> dummy = map.get(posu);
            if(posv==-1){
                dummy.put(v,0);
            }else{
                HashMap<Integer,Integer> dummy2 = map.get(posv);
                dummy.putAll(dummy2);
                map.remove(posv);
            }
        }
  }

  long vreach = 0;
  long ans = 0;
  for( HashMap<Integer,Integer> dummy : map){
      long size = dummy.size();
//      System.out.println(size);
      vreach += size;
      long number = (long)(Math.pow(size,k));
      ans+=number;
  }

  ans += n-vreach;

  ans = (long)(Math.pow(n,k))-ans;
    System.out.println(ans);
}
}
