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.*;
import java.math.*;
public class Main
{
    static ArrayList<Integer> edge[];
    static int dfs(int src,boolean vis[],int cntr)
    {
        vis[src]=true;
        for(int i=0;i<edge[src].size();i++)
        {
            int tp=edge[src].get(i);
            if(!vis[tp])
            {
                cntr=dfs(tp,vis,cntr+1);
            }
        }
        return cntr;
    }
    public static void main(String args[])throws Exception
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw=new PrintWriter(System.out);
        String str[]=br.readLine().split(" ");
        int n=Integer.parseInt(str[0]);
        int k=Integer.parseInt(str[1]);
        //Set<Integer> set=new HashSet<>();
        edge=new ArrayList[n+1];
        for(int i=1;i<=n;i++)
        edge[i]=new ArrayList<>();
        for(int i=0;i<n-1;i++)
        {
            str=br.readLine().split(" ");
            int u=Integer.parseInt(str[0]);
            int v=Integer.parseInt(str[1]);
            int x=Integer.parseInt(str[2]);
            if(x==0)
            {
                edge[u].add(v);
                edge[v].add(u);
            }
        }
        BigInteger big=new BigInteger(Integer.toString(n));
        big=big.pow(k);
        boolean vis[]=new boolean[n+1];
        for(int i=1;i<=n;i++)
        {
            if(!vis[i]&&edge[i].size()>0)
            {
                int nov=dfs(i,vis,1);
                BigInteger temp=new BigInteger(Integer.toString(nov)).pow(k);
                temp=temp.subtract(new BigInteger(Integer.toString(nov)));
                big=big.subtract(temp);
            }
        }
        big=big.subtract(new BigInteger(Integer.toString(n)));
        pw.println(big.mod(new BigInteger("1000000007")));
        pw.flush();
        pw.close();
    }
}