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 c {
	static int mod=1000000007;
	public static void main(String[] args) throws IOException {
		BufferedReader f=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer tk=new StringTokenizer(f.readLine());
		int n=Integer.parseInt(tk.nextToken());
		int k=Integer.parseInt(tk.nextToken());
		
		int uf[]=new int[n];
		for(int i=0;i<n;i++){
			uf[i]=i;
		}
		for(int i=0;i<n-1;i++){
			tk=new StringTokenizer(f.readLine());
			int u=Integer.parseInt(tk.nextToken())-1;
			int v=Integer.parseInt(tk.nextToken())-1;
			int x=Integer.parseInt(tk.nextToken());
			if(x==0){//union the two
				uf[u]=Math.min(uf[u], uf[v]);
				uf[v]=Math.min(uf[u], uf[v]);
			}
		}
		for(int i=n-1;i>=0;i--){
			if(uf[i]!=i)
				compress(uf,i);
		}
		/*for(int i=0;i<n;i++){
			System.out.print(uf[i]);
		}*/
		//System.out.println();
		HashMap<Integer,Integer> setSize=new HashMap<Integer,Integer>();
		for(int i=0;i<n;i++){
			if(!setSize.containsKey(uf[i])){
				setSize.put(uf[i],1);
			}
			else{
				setSize.put(uf[i],setSize.get(uf[i])+1);
			}
		}
		long sum=0;
		for(int i=2;i<=k;i++){ //size of sequence
			sum*=n;
			sum%=mod;
			for(int a:setSize.keySet()){
				long b=setSize.get(a);
				long curr=b*(((long)n)-b);
				curr%=mod;
				for(int j=0;j<i-2;j++){
					curr*=b;
					curr%=mod;
				}
				sum+=curr;
				sum%=mod;
			}
			//System.out.println(sum);
			
		}
		System.out.println(sum);

	}

	private static void compress(int[] uf,int i) {
		if(uf[i]==i) return;
		else{
			compress(uf,uf[i]);
			uf[i]=uf[uf[i]];
			return;
		}
		
	}

}
