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.math.BigInteger;
import java.util.*;
public class C {
	static BufferedReader br;
	static PrintWriter pr;
	static int cin() throws Exception
	{
		return Integer.valueOf(br.readLine());
	}
	static int[] split() throws Exception
	{
		String[] cmd=br.readLine().split(" ");
		int[] ans=new int[cmd.length];
		for(int i=0;i<cmd.length;i++)
		{
			ans[i]=Integer.valueOf(cmd[i]);
		}
		return ans;
	}
	static long[] splitL() throws IOException
	{
		String[] cmd=br.readLine().split(" ");
		long[] ans=new long[cmd.length];
		for(int i=0;i<cmd.length;i++)
		{
			ans[i]=Long.valueOf(cmd[i]);
		}
		return ans;
	}
	static long p=1000000007;
	static long power(long x, long y) 
    { 
        long res = 1;      
        x = x % p;  
       if (x == 0) return 0;
        while (y > 0) 
        { 
            if((y & 1)==1) 
                res = (res * x) % p; 
            y = y >> 1;  
            x = (x * x) % p;  
        } 
        return res; 
    }
	static int[]par;
	static int[]rank;
	static int[]size;
	static int find(int n)
	{
		if(n==par[n])
			return n;
		return par[n]=find(par[n]);
	}
	static void union(int x,int y)
	{
		int p1=find(x);
		int p2=find(y);
		if(p1==p2)
			return;
		if(rank[p1]>rank[p2])
		{
			par[p2]=p1;
			size[p1]+=size[p2];
		}
		else
		{
			par[p1]=p2;
			if(rank[p1]==rank[p2])
				rank[p1]++;
			size[p2]+=size[p1];
		}
	}
	public static void main(String[] args) throws Exception{
		// TODO Auto-generated method stub
		br=new BufferedReader(new InputStreamReader(System.in));
		pr=new PrintWriter(new OutputStreamWriter(System.out));
		int cases=1;
		while(cases!=0)
		{
			cases--;
			int[]arr=split();
			int n=arr[0];
			int k=arr[1];
			par=new int[n+1];
			rank=new int[n+1];
			size=new int[n+1];
			Arrays.fill(size, 1);
			long mod=(long)1e9+7;
			for(int i=0;i<=n;i++)
			{
				par[i]=i;
			}
			int[]mark=new int[n+1];
			int[][]store=new int[n][3];
			for(int i=0;i<n-1;i++)
			{
				store[i]=split();
				if(store[i][2]==0)
					union(store[i][0],store[i][1]);
			}
			long ans=1;
			for(int i=1;i<=k;i++)
			{
				ans=(ans*n)%mod;
			}
			int tot=0;
			for(int i=0;i<n-1;i++)
			{
				if(store[i][2]==1)
					continue;
				int f=find(store[i][0]);
				if(mark[f]==1)
					continue;
				mark[f]=1;
				int y=size[f];
				//System.out.println(f+" "+y+" "+power((long)y,(long)k));
				tot+=y;
				ans=((ans-power((long)y,(long)k))%mod+mod)%mod;
			}
			tot=n-tot;
			ans=((ans-tot)%mod+mod)%mod;
			System.out.println(ans);
		}
	}
}
