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.*;

public class Main{
	public static void main(String[] args){
		Scanner sc=new Scanner(System.in);

		int N=sc.nextInt();
		int K=sc.nextInt();

		HashMap<Integer,ArrayList<Integer>>tree=new HashMap<>();
		int from,to,color;
		for(int i=0;i<N-1;i++){
			from=sc.nextInt();
			to=sc.nextInt();
			color=sc.nextInt();
			if(tree.get(from)==null)tree.put(from,new ArrayList<>());
			if(tree.get(to)==null)tree.put(to,new ArrayList<>());
			if(color==0){
				tree.get(from).add(to);
				tree.get(to).add(from);
			}
		}

		boolean[] vis=new boolean[N+1];
		int temp=0,mod=1_000_000_007,ss,pp;
		for(int i=1;i<=N;i++){
			if(!vis[i]){
				ss=size(tree,vis,i);
				pp=pow(ss,K,mod);
				// System.out.println("ss= "+ss);
				temp=(mod+(temp+pp-ss)%mod);
				// System.out.println("pp= "+pp);
			}
		}
		
// 		System.out.println(temp);
		temp=(mod+(pow(N,K,mod)-temp-N))%mod;
		System.out.println(temp);
	}

	static int size(HashMap<Integer,ArrayList<Integer>>G,boolean[] vis,int v){
		int ans=1;
		vis[v]=true;
		if(G.get(v)!=null){
			for(int x:G.get(v)){
				if(!vis[x])
				ans+=size(G,vis,x);
			}
		}
		return ans;
	}

	static int pow(int base,int exp,int mod){
		long ans=base;
		for(int i=1;i<exp;i++){
			ans=(ans*base)%mod;
		}
		return (int)ans;
	}

}