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.*;
public class SolutionEdgyTree
{
  static ArrayList<Integer> adj[];
  static long cnt;
  static int[] vis;
  static long mod=(long)1e9+7;
  public static void main(String[] args)
  {
    Scanner in=new Scanner(System.in);
    int n=in.nextInt();
    int k=in.nextInt();
    adj=new ArrayList[n];
    for(int i=0;i<n;i++)
    {
      adj[i]=new ArrayList<Integer>();
    }
    for(int i = 0; i < n - 1; ++i) 
    {
      int u = in.nextInt() - 1;
      int v = in.nextInt() - 1;
      int col = in.nextInt();

      if(col == 0) 
      {
        adj[u].add(v);
        adj[v].add(u);
      }
    }
    long ans = (long)fast_pow(n, k);
    long rem = 0;

    vis = new int[n];
    for(int i = 0; i < n; ++i) 
    {
      if(vis[i] == 0) 
      {
        cnt = 0;
        dfs(i);
        rem += (long)fast_pow(cnt, k);
      }
    }
    rem %= mod;
    ans = (ans - rem + mod) % mod;
    System.out.print(ans);
  }
  static void dfs(int i)
  {
    vis[i]=1;
    cnt++;
    for(int j : adj[i])
    {
      if(vis[j] == 0)
        dfs(j);
    }
  }
  static long fast_pow(long a, long b) {
  if(b == 0)
   return 1L;

  long val = fast_pow(a, b / 2);

  if(b % 2 == 0)
   return val * val % mod;
  else 
   return val * val % mod * a % mod;
 }
}