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.
//package com.pb.codeforces.practice;

import java.util.ArrayList;
import java.util.Scanner;

public class CF1139C {
	
	public static int mod = 1000000007;
	public static int cnt = 0;
	
	public static void dfs(int u, ArrayList<Integer>[] adj, boolean[] vi) {
		vi[u] = true;
		cnt++;
		for(int v : adj[u]) {
			if(vi[v]) continue;
			dfs(v,adj,vi);
		}
	}
	
	public static long compute(int n, int k) {
		long ans = 1;
		for(int i=0; i<k; i++) {
			ans = (ans%mod * n%mod)%mod;
		}
		return ans%mod;
	}
	
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt(); int k = in.nextInt();
		ArrayList<Integer>[] adj = new ArrayList[n];
		for(int i=0; i<adj.length; i++)
			adj[i] = new ArrayList<Integer>();
		for(int i=0; i<n-1; i++) {
			int u = in.nextInt()-1; int v = in.nextInt()-1; int b = in.nextInt();
			if(b == 1) continue;
			adj[u].add(v);
			adj[v].add(u);
		}
		boolean[] vi = new boolean[n];
		long tot = compute(n,k)%mod;
		long badSeq = 0;
		for(int i=0; i<n; i++) {
			if(vi[i]) continue;
			cnt = 0;
			dfs(i,adj,vi);
			badSeq = (badSeq%mod + compute(cnt,k)%mod)%mod;
		}
		badSeq%=mod;
		long ans = tot - badSeq;
		if(ans < 0)
			ans += mod;
		System.out.println(ans);
	}
}
