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.
// Created by Whiplash99
import java.io.*;
import java.util.*;
public class C
{
    private static final long MOD=1000000007;
    private static int vis[];
    private static HashMap<Integer,Integer>[] edge;
    private static ArrayDeque<Integer> DQ;

    private static long DFS(int i)
    {
        int count=1,v,x;
        vis[i]=1;

        for(Map.Entry<Integer,Integer> obj:edge[i].entrySet())
        {
            v=obj.getKey();
            x=obj.getValue();

            if(vis[v]==0)
            {
                if(x==1)
                    DQ.add(v);
                else
                    count+=DFS(v);
            }
        }

        return count;
    }

    private static long pow2(long a, long b)
    {
        a%=MOD;
        b%=MOD-1;

        long res=1;

        while(b>0)
        {
            if((b&1)==1)
                res=(res*a)%MOD;

            a=(a*a)%MOD;
            b>>=1;
        }

        return res%MOD;
    }
    public static void main(String[] args) throws IOException
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));

        int i,N,k,u,v,x;
        long count=0,tmp,tmp2,total;

        String s[]=br.readLine().trim().split(" ");
        N=Integer.parseInt(s[0]);
        k=Integer.parseInt(s[1]);

        vis=new int[N+1];
        edge=new HashMap[N+1];
        DQ=new ArrayDeque<>();
        for(i=0;i<=N;i++)
            edge[i]=new HashMap<>();

        total=pow2(N,k);

        for(i=1;i<=N-1;i++)
        {
            s=br.readLine().trim().split(" ");
            u=Integer.parseInt(s[0]);
            v=Integer.parseInt(s[1]);
            x=Integer.parseInt(s[2]);

            edge[u].put(v,x);
            edge[v].put(u,x);
        }

        DQ.add(1);
        while(!DQ.isEmpty())
        {
            tmp=DFS(DQ.poll());
            tmp2=pow2(tmp,k);
            count=(count+tmp2)%MOD;
        }

        total-=count;
        while(total<0)
            total+=MOD;

        System.out.println(total);
    }


}