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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.LinkedList;
import java.util.Queue;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader sc = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        solver.solve(1, sc, out);
        out.close();
    }

    static class Task {
    	public static final long Mod=(long)1e9+7;
    	public ArrayList<Integer>[] buf;
    	public ArrayList<Node>[] edge;
    	public boolean[] vis;
    	
    	public long quickPow(long x,long y) {
    		long res=1;
    		
    		while(y>0) {
    			if((y&1)==1)
    				res=res*x%Mod;
    			y>>=1;
    			x=x*x%Mod;
    		}
    		
    		return res;
    	}
    	
    	public void bfs(int begin) {
    		Queue<Integer> que=new LinkedList<Integer>();
    		que.offer(begin);
    		
    		while(!que.isEmpty()) {
    			int u=que.poll();
    			if(vis[u])
    				continue;
    			vis[u]=true;
    			buf[begin].add(u);
    			for(Node temp:edge[u]) {
    				int v=temp.index;
    				boolean color=temp.color;
    				if(color)
    					continue;
    				if(!vis[v])
    				    que.offer(v);
    			}
    		}
    	}
    	
        public void solve(int testNumber, InputReader sc, PrintWriter out) {
            int n=sc.nextInt();
            int k=sc.nextInt();
            buf=new ArrayList[n+1];
            edge=new ArrayList[n+1];
            vis=new boolean[n+1];
            
            for(int i=0;i<=n;i++) {
            	buf[i]=new ArrayList<Integer>();
            	edge[i]=new ArrayList<Node>();
            }
            for(int i=0;i<n-1;i++) {
            	int u=sc.nextInt();
            	int v=sc.nextInt();
            	boolean color=sc.nextInt()==1?true:false;            //true black   false rede
            	edge[u].add(new Node(v,color));
            	edge[v].add(new Node(u,color));
            }
            for(int i=1;i<=n;i++) {
            	if(!vis[i])
            		bfs(i);
            }
            long ans=quickPow(n,k);
            long temp=0;
            for(int i=1;i<=n;i++)
            	temp=(temp+quickPow(buf[i].size(),k))%Mod;
            ans=(ans-temp+Mod)%Mod;
            out.println(ans);
        }
    }
    
    static class Node{
    	public int index;
    	public boolean color;
    	
    	public Node(int index,boolean color) {
    		this.index=index;
    		this.color=color;
    	}
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

    }
}
