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 CF_1110 {

    static long power(long x, long y, long p) 
    { 
        // Initialize result 
        long res = 1;      
         
        // Update x if it is more   
        // than or equal to p 
        x = x % p;  
      
        while (y > 0) 
        { 
            // If y is odd, multiply x 
            // with result 
            if((y & 1)==1) 
                res = (res * x) % p; 
      
            // y must be even now 
            // y = y / 2 
            y = y >> 1;  
            x = (x * x) % p;  
        } 
        return res; 
    } 
    static boolean[] vis = new boolean[100007] ;
    static long dfs(int u , int p){
        vis[u] = true ;
        long cnt = 0;
        for(int v : adj[u]){
            if(v == p) continue ;
            cnt = (cnt + dfs(v, u))%MOD ; 
        }
        return (cnt + 1)%MOD ;
    }
    static long MOD = 1000000007 ;
    static ArrayList<Integer>[] adj = new ArrayList[100007] ;
     public static void main(String[] args) {
        FastReader scn = new FastReader() ;
        int n  = scn.nextInt() , k = scn.nextInt();
        for(int i = 0 ;i <= n ;i++){
            adj[i] = new ArrayList<>() ;
        }
        for(int i = 0 ; i < n - 1 ;i++){
            int u = scn.nextInt() , v = scn.nextInt() ;
            int c = scn.nextInt() ;
            if(c == 0){
                adj[u].add(v) ;
                adj[v].add(u) ;
            }
        }
        long ans = 0 ;
        for(int i = 1 ; i <= n ;i++){
            if(!vis[i]){
                long x = dfs(i, 0) ;
                ans = (ans + power(x, k, MOD)) % MOD ;
            }
        }
        long a = power(n, k, MOD) ;
        long f = (a - ans +MOD)%MOD ;
        System.out.println(f);
       
        
     }
     
     
     
     
     static class FastReader 
     { 
         BufferedReader br; 
         StringTokenizer st; 
   
         public FastReader() 
         { 
             br = new BufferedReader(new
                      InputStreamReader(System.in)); 
         } 
   
         String next() 
         { 
             while (st == null || !st.hasMoreElements()) 
             { 
                 try
                 { 
                     st = new StringTokenizer(br.readLine()); 
                 } 
                 catch (IOException  e) 
                 { 
                     e.printStackTrace(); 
                 } 
             } 
             return st.nextToken(); 
         } 
   
         int nextInt() 
         { 
             return Integer.parseInt(next()); 
         } 
   
         long nextLong() 
         { 
             return Long.parseLong(next()); 
         } 
   
         double nextDouble() 
         { 
             return Double.parseDouble(next()); 
         } 
   
         String nextLine() 
         { 
             String str = ""; 
             try
             { 
                 str = br.readLine(); 
             } 
             catch (IOException e) 
             { 
                 e.printStackTrace(); 
             } 
             return str; 
         } 
     } 
     
 }