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 Main;

import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Iterator;
import java.util.Scanner;

public class Main {
	static int maxn = 1000010; 
	static int mod = 1000000007; 
	static int[] pre = new int[maxn];
	static int[] siz = new int[maxn];
	public static void init(){
		for(int i=0;i<maxn;i++){
			pre[i]=i;
			siz[i]=0;
		}
	}
	public static int find(int x){
		if(pre[x]==x) return x;
		return pre[x]=find(pre[x]);
	}
	public static void unite(int a,int b){
		int fx=find(a);
		int fy=find(b);
		if(fx!=fy) pre[fx]=fy;
	}
	public static long qpow(long a,long b){
		long res=1;
		while(b>0){
			if(b%2==1) res=res*a%mod;
			a=a*a%mod;
			b/=2;
		}
		return res%mod;
	}
	public static void main(String[] args) {
		Scanner input = new Scanner(System.in);
		init();
		int n = input.nextInt();
		int k = input.nextInt();
		for(int i=1;i<n;i++){
			int a=input.nextInt();
			int b=input.nextInt();
			int c=input.nextInt();
			if(c==0) unite(a,b);
		}
		long ans=qpow(n,k);
		for(int i=1;i<=n;i++) siz[find(i)]++;
		int cnt=0;
		for(int i=1;i<=n;i++){
			if(pre[i]==i){
				cnt+=siz[i];
				ans=(ans-qpow(siz[i],k)+mod)%mod;
			}
		}
		ans=(ans-(n-cnt)+mod)%mod;
		ans=(ans+mod)%mod;
		System.out.println(ans);
	}
}
