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.BufferedReader; 
import java.io.InputStreamReader; 
import java.util.StringTokenizer; 
import java.io.IOException; 
import java.math.*;


public class cp{

    static long pow(long x, long y, long p){ 

        // Initialize result 
        long res = 1;      
         
        // Update x if it is more   
        // than or equal to p 
        x = x % p;  
      
        while (y > 0) 
        { 
            // If y is odd, multiply x 
            // with result 
            if((y & 1)==1) 
                res = (res * x) % p; 
      
            // y must be even now 
            // y = y / 2 
            y = y >> 1;  
            x = (x * x) % p;  
        } 
        return res; 
    }

    public static void main(String[] args) throws IOException{

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer s = new StringTokenizer(br.readLine());
        
        int n = Integer.parseInt(s.nextToken());

        int k = Integer.parseInt(s.nextToken());

        ArrayList[] adjList = new ArrayList[n];
        for(int i = 0;i < n; i ++){
            adjList[i] = new ArrayList<Integer>();
        }
        for(int i = 0; i < n - 1; i ++){
            s = new StringTokenizer(br.readLine());
            int a = Integer.parseInt(s.nextToken()) - 1;
            int b = Integer.parseInt(s.nextToken()) - 1;   
            int c = Integer.parseInt(s.nextToken());

            if(c == 0){
                adjList[a].add(b);
                adjList[b].add(a);
            }
        }

        boolean[] visited = new boolean[n];
        ArrayList components = new ArrayList();
        for(int i = 0; i < n; i ++){
            if(visited[i]){
                continue;
            }

            Stack stack = new Stack();
            stack.push(i);
            visited[i] = true;
            int count = 0;
            while(!stack.isEmpty()){
                int curr = (int)stack.pop();
                count += 1;

                for(int j = 0; j < adjList[curr].size(); j ++){
                    if(visited[(int)adjList[curr].get(j)]){
                        continue;
                    }

                    stack.push((int)adjList[curr].get(j));
                    visited[(int)adjList[curr].get(j)] = true;
                }
            }

            components.add(count);
        }


        long ans = pow(n, k, 1000000007);
        // System.out.println(ans + " " + n + k);
        for(int i = 0; i < components.size(); i ++){

            ans = (ans - pow((int)components.get(i), k, 1000000007));
            if( ans < 0){
                ans = 1000000007 + ans;
            }
            // System.out.println(ans);
        }

        System.out.println(ans);
    }
}
