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 Solution {
	public static void main (String[] args) throws IOException{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in)); 
		String[] temp=br.readLine().trim().split(" ");
		int V=Integer.parseInt(temp[0]);
		int k=Integer.parseInt(temp[1]);
		
		DSU graph=new DSU(V);
		for(int i=1;i<V;i++)
		{
		    temp=br.readLine().trim().split(" ");
		    int u=Integer.parseInt(temp[0]);
		    int v=Integer.parseInt(temp[1]);
		    int color=Integer.parseInt(temp[2]);
		    if(color==0){
		        graph.makeUnion(u,v);
		    }
		}
		int notGoodSequences=0;
		int mod=1000000009;
		boolean[] marked=new boolean[V+1];
		for(int i=1;i<=V;i++){
		    int parent=graph.getParent(i);
		    if(marked[parent]==false){
		        marked[parent]=true;
		        int size=graph.componentSize(i);
		        notGoodSequences=(int)(0L+notGoodSequences+aPowerBModC(size,k,mod))%mod;
		    }
		}
		int ans=(aPowerBModC(V,k,mod)-notGoodSequences+mod)%mod;
		System.out.println(ans);
	}
	public static int aPowerBModC(int a,int b,int c){
	    if(b==0){
	        return 1;
	    }
	    int smallAns=aPowerBModC(a,b/2,c);
	    int ans=(int)(1L*smallAns*smallAns)%c;
	    if(b%2!=0){
	        ans=(int)(1L*ans*(a%c))%c;
	    }
	    return ans;
	}
}
class DSU{
    private int[] parent;
    private int[] size;
    
    public DSU(int V)
    {
        parent=new int[V+1];
        size=new int[V+1];
        for(int i=1;i<=V;i++)
        {
            parent[i]=i;
            size[i]=1;
        }
    }
    public int getParent(int vertex)
    {
        int temp=vertex;
        while(parent[vertex]!=vertex){
            vertex=parent[vertex];
        }
        parent[temp]=vertex;
        return vertex;
    }
    public void makeUnion(int u,int v){
        int parent1=getParent(u);
        int parent2=getParent(v);
        
        if(parent2==parent1)
        {
            return;
        }
        int size1=size[parent1];
        int size2=size[parent2];
        
        if(size2<size1){
            parent[parent2]=parent1;
            size[parent1]+=size[parent2];
        }
        else{
            parent[parent1]=parent2;
            size[parent2]+=size[parent1];
        }
    }
    public int numComponents(){
        int ans=0;
        int V=this.parent.length-1;
        for(int i=1;i<=V;i++){
            if(this.parent[i]==i){
                ans++;
            }
        }
        return ans;
    }
    public int componentSize(int vertex){
        int parent=getParent(vertex);
        return size[parent];
    }
}