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.io.*;
import java.math.*;
import java.util.*;


// @author : Dinosparton 

public class test {
	 
	   static class Pair{ 
		   long x;
		   long y;
		   
		   Pair(long x,long y){ 
			   this.x = x;
			   this.y = y;
			   
		   }
	   }
	  
	   static class Sort implements Comparator<Pair>
	   {

	       @Override
	       public int compare(Pair a, Pair b)
	       {
	           if(a.x!=b.x)
	           {
	               return (int)(a.x - b.x);
	           }
	           else
	           {
	               return (int)(a.y-b.y);
	           }
	       }
	   }
	   
	   static class Compare { 
		   
		     void compare(Pair arr[], int n) 
		    { 
		        // Comparator to sort the pair according to second element 
		        Arrays.sort(arr, new Comparator<Pair>() { 
		            @Override public int compare(Pair p1, Pair p2) 
		            { 
		            	if(p1.x!=p2.x) {
		                return (int)(p1.x - p2.x); 
		            	}
		            	else { 
		            		return (int)(p1.y - p2.y);
		            	}
		            } 
		        }); 
		  
//		        for (int i = 0; i < n; i++) { 
//		            System.out.print(arr[i].x + " " + arr[i].y + " "); 
//		        } 
//		        System.out.println(); 
		    } 
		} 
	 
	   static class Scanner {
	        BufferedReader br;
	        StringTokenizer st;
	 
	        public Scanner()
	        {
	            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;
	        }
	    }
	
	  static long MOD = 1000000007;
	  
	  static long pow (long a , long b) { 
		  
		  long ans = 1;
		  
		  for(int i=1;i<=b;i++) { 
			  
			  ans = ans*a;
			  ans = (ans + MOD) %MOD;
		  }
		  
		  return (ans+MOD)%MOD;
	  }
	  
	  static int dfs(int cur,boolean visited[],ArrayList<Integer> graph[]) { 
		  
		  int cnt = 1;
		  
		  visited[cur] = true;
		  
		  for(int i : graph[cur]) { 
			  
			  if(!visited[i]) { 
				  cnt += dfs(i,visited,graph);
			  }
		  }
		  
		  return cnt;
	  }
	   public static void main(String args[]) throws Exception { 
		
		   
		   Scanner sc = new Scanner();
		   StringBuilder res = new StringBuilder();
		  
		  
		   int tc = 1;
		  
		   while(tc-->0) { 
			
			int n = sc.nextInt();
			int k = sc.nextInt();
			
			ArrayList<Integer> graph[] = new ArrayList[n+1];
			
			for(int i=1;i<=n;i++) { 
				graph[i] = new ArrayList<>();
			}
			
			for(int i=0;i<n-1;i++) { 
				
				int u = sc.nextInt();
				int v = sc.nextInt();
				int e = sc.nextInt();
				
				if(e==0) { 
					graph[u].add(v);
					graph[v].add(u);
				}
				
			}
			
			long ans = pow(n,k);
			long min = 0;
			boolean visited[] = new boolean[n+1];
			
			for(int i=1;i<=n;i++) { 
				
				int cnt = 0;
				
				if(!visited[i]) { 
					cnt  = dfs(i,visited,graph);
				}
				
				min += pow(cnt,k);
				min = min%MOD;
			}
			
			ans = ans - min;
			ans = (ans+MOD)%MOD;
			
			System.out.println(ans);
		   }
		   
		   System.out.println(res);
	   }
}  




