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.io.*;
import java.util.*;
public class Graphs {
	
	public static int mod=1000000007;
	
	public static long poweraftermod(int a, int b, int mod)
	{
		//this will return (a^b)%mod
		long prod=1;
		for (int i=0;i<b;i++)
		{
			prod=((prod%mod)*(a%mod))%mod;
		}
		return prod%mod;
	}
	
	public static int dfs(HashMap<Integer,HashSet> adj, int currvertex, boolean visited[])
	{
		if (visited[currvertex]==true)
			return 0;
		visited[currvertex]=true;
		HashSet<Integer> set=adj.get(currvertex);
		int ans=1;
		for (int i: set)
		{
			if (visited[i]==true)
				continue;
			ans+=dfs(adj, i, visited);
		}
		return ans;
	}

	public static void main(String[] args) throws Exception{
	
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		String inp[]=br.readLine().split(" ");
		int n=Integer.parseInt(inp[0]);
		int k=Integer.parseInt(inp[1]);
		HashMap<Integer, HashSet> map=new HashMap<>();
		for (int i=0;i<n;i++)
		{
			HashSet<Integer> arr=new HashSet<>();
			map.put(i, arr);
		}
		HashSet<Integer> s=new HashSet<>();
		for (int i=0;i<n-1;i++)
		{
			inp=br.readLine().split(" ");
			int u=Integer.parseInt(inp[0])-1;
			int v=Integer.parseInt(inp[1])-1;
			int edge=Integer.parseInt(inp[2]);
			if (edge==0)
			{
				map.get(u).add(v);
				map.get(v).add(u);
			}
			s.add(u);
			s.add(v);
		}
		
		long ans=0;
		boolean visited[]=new boolean[n];
		//count number of all red paths
		long allpaths=poweraftermod(n,k,mod);
		for (int i : s)
		{
			if (visited[i]==true)
				continue;
			int ans1= dfs(map, i, visited);
			visited[i]=true;
			allpaths-=poweraftermod(ans1%mod, k, mod)%mod;
			allpaths+=mod;
			allpaths%=mod;
		}
		System.out.println((allpaths)%mod);
	}
}
