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 C 
{	
	static ArrayList<Integer> g[];
	static int[] vis,cc;
	static long mod=(long)1e9 + 7;
	
	public static void main(String[] args)throws IOException 
	{	
		
		FastReader f=new FastReader();
		StringBuffer sb=new StringBuffer();
	
		int n=f.nextInt();
		int k=f.nextInt();
		
		g=new ArrayList[n+1];
		vis=new int[n+1];
		cc=new int[n+1];
		
		for(int i=1;i<=n;i++)
			g[i]=new ArrayList<Integer>();
		
		for(int i=1;i<n;i++)
		{
			int x=f.nextInt();
			int y=f.nextInt();
			int col=f.nextInt();
			
			if(col==0)
			{
				g[x].add(y);
				g[y].add(x);
			}
		}
		int count=1;
		for(int i=1;i<=n;i++)
		{	
			if(vis[i]==0)
			{
				dfs(i,count);
				count++;
			}
		}
		Map<Integer,Integer> map=new HashMap<>();
		
		for(int i=1;i<=n;i++)
		{
			int val=cc[i];
			if(map.containsKey(val))
				map.put(val,map.get(val)+1);
			else
				map.put(val,1);
		}
//		System.out.println("map = "+map);
		long ans=fastPow(n,k);
//		System.out.println("ans ini = "+ans);
		for(int key : map.keySet())
		{
			int val=map.get(key);
			// val^k
			long sub=fastPow((long)val,(long)k)%mod;
			ans=(ans-sub)%mod ;
//			System.out.println("sub : "+sub);
		}
		if(ans<0)
			ans=mod+ans;
		System.out.println(ans);
	}
	static void dfs(int n,int count)
	{
		vis[n]=1;
		cc[n]=count;
		
		for(int child : g[n])
		{
			if(vis[child]==0)
				dfs(child,count);
		}
	}
	static long fastPow(long n, long m) {
		long res = 1L;
		
		while (m > 0) {
			if ((m & 1) != 0) {
				res=((res%mod)*(n%mod))%mod;
				m--;
			} else {
				n=(n%mod * n%mod)%mod;
				m /= 2;
			}
		}
		return res;
	}
}

class FastReader 
{ 
	BufferedReader br; 
    StringTokenizer st; 

    public FastReader() {
    	br = new BufferedReader(new
                 InputStreamReader(System.in)); 
    }
    String next() { 
        while (st == null || !st.hasMoreElements()) { 
            try{ 
                st = new StringTokenizer(br.readLine()); 
	            } 
	            catch (IOException  e) { 
	                e.printStackTrace(); 
	            } 
	    } 
	    return st.nextToken(); 
	} 
	int nextInt() { 
		return Integer.parseInt(next()); 
	} 
	long nextLong() { 
		return Long.parseLong(next()); 
	} 
	double nextDouble() { 
	    return Double.parseDouble(next()); 
	} 
	String nextLine() { 
	    String str = ""; 
	    try{ 
	        str = br.readLine(); 
	    } 
	    catch (IOException e) { 
	            e.printStackTrace(); 
	    } 
	    return str; 
    } 
} 
