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.*;
public final class Codechef {
    static int mod = (int)(1e9+7);
    static int pow(int a, int b) {
        int res = 1;
        while(b>0) {
            if(b%2!=0) 
                res = (res*a)%mod;
            a = (a*a)%mod;
            b>>=1;
        }
        return res%mod;
    }
    static int n;
    static boolean[] visited;
    static ArrayList<Integer>[] adj;
    static int dfs(int src) {
        visited[src] = true;
        int count = 1;
        Stack<Integer> stack = new Stack<>();
        stack.push(src);
        while(!stack.isEmpty()) {
            int curr = stack.pop();
            for(int i: adj[src]) {
                if(!visited[i]) {
                    stack.push(i);
                    visited[i] = true;
                    count++;
                }
            }
        }
        return count;
    }
    @SuppressWarnings("unchecked")
    public static void main (String[] args) {
        Scanner sc = new Scanner(System.in);
        n = sc.nextInt();
        int k = sc.nextInt();
        adj = new ArrayList[n];
        visited = new boolean[n];
        for(int i = 0; i<n; i++) adj[i] = new ArrayList<>();
        for(int i = 0; i<n-1; i++) {
            int u = sc.nextInt()-1;
            int v = sc.nextInt()-1;
            boolean black = sc.nextInt()==1;
            if(!black) {
                adj[u].add(v);
                adj[v].add(u);
            }
        }
        int ans = pow(n, k);
        for(int i = 0; i<n; i++) {
            if(!visited[i]) 
                ans-=pow(dfs(i), k);
        }
        System.out.println(ans);
    }
}