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.
//package com.company;
import java.util.*;
public class Main {

    public static void main(String[] args) {
        // write your code here

        Scanner s=new Scanner(System.in);StringBuilder sb=new StringBuilder();
     int n=s.nextInt();
     int k=s.nextInt();ArrayList<Integer> [] a=new ArrayList[n+1];HashMap<Integer,Integer> [] val=new HashMap[n+1];
     for(int i=0;i<n-1;i++){
         int u=s.nextInt();int v=s.nextInt();int x=s.nextInt();
         if(a[u]==null) a[u]=new ArrayList<Integer>();
         if(a[v]==null) a[v]=new ArrayList<Integer>();
         if(val[u]==null) val[u]=new HashMap<Integer, Integer>();
         if(val[v]==null) val[v]=new HashMap<Integer, Integer>();
         a[u].add(v);a[v].add(u);val[v].put(u,x);
val[u].put(v,x);
     }vis=new int[n+1];long sum=0;
     for(int i=1;i<=n;i++){
         if(vis[i]==0){count=0;dfs(i,val,a);
         sum=(sum%1000000007+(long)Math.pow(count,k)%1000000007)%1000000007;}
     }
        System.out.println((long)(Math.pow(n,k)%1000000007-sum%1000000007)%1000000007);
    }static int[] vis;static int count;
    static void dfs(int i,HashMap<Integer,Integer> [] val,ArrayList<Integer> []a) {
            vis[i]=1;count++;
            if(a[i]!=null){
                for(int j:a[i]){
                    if(vis[j]==0&&val[j].get(i)!=1){
                        dfs(j,val,a);
                    }
                }
            }
    }
}


class Student
{
    int rollno,x,pos;
//    String name, address;

    // Constructor
    public Student(int rollno, int x,int pos)
    {
        this.rollno = rollno;
        this.x=x;this.pos=pos;
    }

    // Used to print student details in main()
    public String toString()
    {
        return this.rollno + " " +this.x;
    }
}

class Sortbyroll implements Comparator<Student>
{
    // Used for sorting in ascending order of
    // roll number
    public int compare(Student a, Student b)
    {
        return  b.x-a.x;
    }
}