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 Main {
    public static long bfs(ArrayList<ArrayList<Integer>> a, int root, boolean[] visited) {
        long count=0;
        Queue<Integer> q = new LinkedList<>();
        visited[root] = true;
        q.add(root);
        while (!q.isEmpty()) {
            int u = q.poll();
            count++;
            for (int i = 0; i < a.get(u).size(); i++) {
                if (!visited[a.get(u).get(i)]) {
                    visited[a.get(u).get(i)] = true;
                    q.add(a.get(u).get(i));
                }
            }
        }
        return count;
    }
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw = new PrintWriter(System.out);
        String[] s = br.readLine().split(" ");
        int n = Integer.parseInt(s[0]),k=Integer.parseInt(s[1]);
        long ans = (long)Math.pow(n,k)%1000000007;
        ArrayList<ArrayList<Integer>> a = new ArrayList<>();
        for(int i=0;i<n;i++) a.add(new ArrayList<>());
        for(int i=0;i<n-1;i++){
            s = br.readLine().split(" ");
            int src = Integer.parseInt(s[0])-1,dest = Integer.parseInt(s[1])-1,edge = Integer.parseInt(s[2]);
            if(edge==0) {
                a.get(src).add(dest);
                a.get(dest).add(src);
            }
        }
        boolean[] visited = new boolean[n];
        for(int i=0;i<n;i++) {
            if (!visited[i]) {
                ans -= ((long) Math.pow(bfs(a, i, visited),k) % 1000000007);
            }
        }
        pw.println(ans);
        pw.flush();
        pw.close();
    }
}