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.util.*;

public class Main{
	
	static long mod=1000000007;
	
	public static void main(String[] args) throws IOException {
		Writer out=new Writer(System.out);
		Reader in=new Reader(System.in);
		int t=1;
		while(t-->0) {		
			int n=in.nextInt();
			int k=in.nextInt();
			long total=pow(n,k);
			ArrayList<Integer> [] gr=new ArrayList[n];
			for(int i=0; i<n; i++) gr[i]=new ArrayList<>();
			for(int i=0; i<n-1; i++) {
				int x=in.nextInt()-1;
				int y=in.nextInt()-1;
				int c=in.nextInt();
				if(c==0) {
					gr[x].add(y);
					gr[y].add(x);
				}				
			}
			boolean vis[]=new boolean[n];
			for(int i=0; i<n; i++) {
				if(!vis[i]) {
					long g=dfs(gr,vis,i);
					total=(total-pow(g,k))%mod;
				}
			}
			out.println(total);
		}
		out.close();		
	}
	
	static long dfs(ArrayList<Integer> [] gr, boolean [] vis, int n) {
		
		long g=1;
		vis[n]=true;
		for(int i=0; i<gr[n].size(); i++) {
			if(!vis[gr[n].get(i)]) {
				g=(g+dfs(gr,vis,gr[n].get(i)))%mod;
			}
		}
		return g;
	}
	
	static long pow(long n, long k) {
		if(k==0) return 1;
		if(k==1) return n;
		long temp=pow(n,k/2);
		temp=(temp*temp)%mod;
		if(k%2==0) return temp%mod;
		return (temp*n)%mod;
	}
	
/**************************************************** UTILITY CODE BELOW ***********************************************************/	
	
	static void sort(int[] a) {
		ArrayList<Integer> list=new ArrayList<>();
		for (int i:a) list.add(i);
		Collections.sort(list);
		for (int i=0; i<a.length; i++) a[i]=list.get(i);
	}
	
	static class Reader{
		
		BufferedReader br;
		StringTokenizer to;
		
		Reader(InputStream stream){
			br=new BufferedReader(new InputStreamReader(stream));
			to=new StringTokenizer("");
		}
		
		String next() {
			while(!to.hasMoreTokens()) {
				try {
					to=new StringTokenizer(br.readLine());	
				}catch(IOException e) {}
				
			}
			return to.nextToken();
			
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		
		long nextLong() {
			return Long.parseLong(next());
		}
		
		int [] readArray(int n) {
			int a[]=new int[n];
			for(int i=0; i<n ;i++) a[i]=nextInt();
			return a;
		}
		long [] readLongArray(int n) {
			long a[]=new long[n];
			for(int i=0; i<n ;i++) a[i]=nextLong();
			return a;
		}
		
	}
	
	static class Writer extends PrintWriter{
		Writer(OutputStream stream){
			super(stream);
		}
		void println(int [] array) {
			for(int i=0; i<array.length; i++) {
				print(array[i]+" ");
			}
			println();
		}
	}
	
}