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.io.*;
import java.util.*;
public class Solution
{
    static ArrayList<Integer> adj[];
    static boolean visited[];
    static int N,K;
    static int mod=(int)1e9+7;
    public static void main(String ag[])
    {
        Scanner sc=new Scanner(System.in);
        int i,j,k;
        N=sc.nextInt();
        K=sc.nextInt();
        
        visited=new boolean[N+1];
        adj=new ArrayList[N+1];
        for(i=0;i<=N;i++)
        adj[i]=new ArrayList<>();
        
        for(i=1;i<N;i++)
        {
            int a=sc.nextInt();
            int b=sc.nextInt();
            int c=sc.nextInt();
            
            if(c==0)
            {
                adj[a].add(b);
                adj[b].add(a);
            }
        }
        
        long total=power(N,K);
        for(i=1;i<=N;i++)
        {
            if(!visited[i])
            {
                total=(total%mod-power(DFS(i),K)+mod)%mod;
            }
        }
        System.out.println(total);
    }
    public static long power(long a,long b)
    {
        long res=1L;
        while(b>0)
        {
            if((b&1)==1)
            res=(res%mod*a%mod)%mod;
            a=(a%mod*a%mod)%mod;
            b=b>>1;
        }
        return res;
    }
    public static int DFS(int node)
    {
        visited[node]=true;
        int cnt=1;
        Iterator<Integer> itr=adj[node].iterator();
        while(itr.hasNext())
        {
            int next=itr.next();
            if(!visited[next])
            {
                cnt+=DFS(next);
            }
        }
        return cnt;
    }
    
}