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.ArrayList;
import java.util.Scanner;

public class Edges {
	public static long mod = 1000000007;
	public static ArrayList<ArrayList<Integer>> list;
	public static int vis[];
	static long count = 0;
	public static long fast_pow(long a, long b) {
		if(b == 0)
			return 1L;
 
		long val = fast_pow(a, b / 2);
 
		if(b % 2 == 0)
			return val * val % mod;
		else 
			return val * val % mod * a % mod;
	}
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int k = sc.nextInt();
		list =  new ArrayList<ArrayList<Integer>>(n);
		for (int i = 0; i<=n; i++) {
			list.add(new ArrayList<Integer>());
		}
		vis =  new int[n+1];
		for (int i = 0; i < n-1; i++) {
			int u = sc.nextInt();
			int v = sc.nextInt();
			int c = sc.nextInt();
			if(c==0) {
				list.get(u).add(v);
				list.get(v).add(u);
			}
		}
		long total = fast_pow(n, k)%mod;
		long rem = 0;
		for (int i = 1; i <=n; i++) {
			if(vis[i]==0) {
			count  = 0;
			dfs(i);
			rem = (rem%mod + (fast_pow(count,k))%mod)%mod;
			}
		}
		System.out.println((total-rem+mod)%mod);
	}

	private static void dfs(int i) {
		vis[i] = 1;
		count++;
		for (Integer e : list.get(i)) {
			if(vis[e]==0) {
				dfs(e);
			}
		}
		
	}

}
