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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.LinkedList;
import java.util.List;
import java.util.StringTokenizer;


public class C{
	
	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; 
        } 
    }
	static LinkedList<Integer> ar[];
	static boolean vis[];
	static long count;
	public static void dfs(int i)
	{	
		count++;
		vis[i] = true;
		
		for(int n:ar[i])
		{
			if(!vis[n])
			{
				dfs(n);
			}
		}
	}
	static long prime = (long) (1e9+7);
	public static void main(String[] args) 
	{
		OutputStream outputStream = System.out;
        FastReader sc = new FastReader();
        PrintWriter out = new PrintWriter(outputStream);
     
        int n = sc.nextInt();
        int k = sc.nextInt();
        ar = new LinkedList[n];
        for(int i = 0; i <= n-1; i++)
        {
        	ar[i] = new LinkedList<>();
        }
        for(int i = 0; i < n-1; i++)
        {
        	int s = sc.nextInt();
        	int e = sc.nextInt();
        	int c = sc.nextInt();
        	if(c == 1) continue;
        	
        	ar[s-1].add(e-1);
        	ar[e-1].add(s-1);
        }
        
        vis = new boolean[n];
        long tCount = 0;
        Arrays.fill(vis, false);
        for(int i = 0; i < n; i++)
        {
        	if(!vis[i])
        	{	
        		count = 0;
        		dfs(i);
        		//out.println(count);
        		count = (long) (Math.pow(count,k));
        		//out.println(count);
        		tCount = (tCount+count)%prime;
        	}
        }
        /*int minus = 0;
        for(int i = 0; i < n; i++)
        {
        	if(!vis[i])
        	{	
        		out.println(i);
        		minus++;
        	}
        }
        out.println("minus "+minus);
        out.println("tcount "+tCount);
        */
        long ans = (long)Math.pow(n,k)%prime;
        //out.println("ans "+ans);
        //ans = ans-minus;
        ans = (long)(ans-tCount)%prime;
        out.println(ans);
        out.close();
	}

}
