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.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;

public class Solution 
{
	static class InputReader
	{
	    private final InputStream stream;
	    private final byte[] buf = new byte[8192];
	    private int curChar, snumChars;

	    public InputReader(InputStream st) {
	      this.stream = st;
	    }

	    public int read() {
	      if (snumChars == -1)
	        throw new InputMismatchException();
	      if (curChar >= snumChars) {
	        curChar = 0;
	        try {
	          snumChars = stream.read(buf);
	        } catch (IOException e) {
	          throw new InputMismatchException();
	        }
	        if (snumChars <= 0)
	          return -1;
	      }
	      return buf[curChar++];
	    }

	    public int nextInt() {
	      int c = read();
	      while (isSpaceChar(c)) {
	        c = read();
	      }
	      int sgn = 1;
	      if (c == '-') {
	        sgn = -1;
	        c = read();
	      }
	      int res = 0;
	      do {
	        res *= 10;
	        res += c - '0';
	        c = read();
	      } while (!isSpaceChar(c));
	      return res * sgn;
	    }

	    public long nextLong() {
	      int c = read();
	      while (isSpaceChar(c)) {
	        c = read();
	      }
	      int sgn = 1;
	      if (c == '-') {
	        sgn = -1;
	        c = read();
	      }
	      long res = 0;
	      do {
	        res *= 10;
	        res += c - '0';
	        c = read();
	      } while (!isSpaceChar(c));
	      return res * sgn;
	    }

	    public int[] nextIntArray(int n) {
	      int a[] = new int[n];
	      for (int i = 0; i < n; i++) {
	        a[i] = nextInt();
	      }
	      return a;
	    }

	    public String readString() {
	      int c = read();
	      while (isSpaceChar(c)) {
	        c = read();
	      }
	      StringBuilder res = new StringBuilder();
	      do {
	        res.appendCodePoint(c);
	        c = read();
	      } while (!isSpaceChar(c));
	      return res.toString();
	    }

	    public String nextLine() {
	      int c = read();
	      while (isSpaceChar(c))
	        c = read();
	      StringBuilder res = new StringBuilder();
	      do {
	        res.appendCodePoint(c);
	        c = read();
	      } while (!isEndOfLine(c));
	      return res.toString();
	    }

	    public boolean isSpaceChar(int c) {
	      return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	    }

	    private boolean isEndOfLine(int c) {
	      return c == '\n' || c == '\r' || c == -1;
	    }
	}
  public static class pair
    {
        int val,level;
        public pair(int a,int b)
        {
            this.val = a;
            this.level = b;
        }
    }
   public static class graph
    {
        public LinkedList<Integer>[] adj;
        public int size;
        public int count;
        public graph(int n)
        {
            this.size = n;
            this.count = 0;
            adj = new LinkedList[n+1];
            for(int i=0;i<=n;i++)
                adj[i] = new LinkedList<>();
        }
        public void add(int u,int v)
        {
            adj[u].add(v);
            adj[v].add(u);
        }
        public void dfs(int src,boolean[] vis)
        {
            vis[src] = true;
            count++;
            Iterator<Integer> it = adj[src].iterator();
            while(it.hasNext())
            {
                int n = it.next();
                if(!vis[n])
                    dfs(n,vis);
            }
        }
        public void print()
        {
            for(int i=0;i<=size;i++)
            {
                System.out.print(i + " --> ");
                Iterator<Integer> it = adj[i].iterator();
                while(it.hasNext())
                {
                    int n = it.next();
                    System.out.print(n + ", ");
                }
                System.out.println();
            }
        }
    }
    public static void main(String[] args) throws Exception
    {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);
       	String[] str = (br.readLine()).trim().split(" ");
        int n = Integer.parseInt(str[0]);
        int k = Integer.parseInt(str[1]);
        graph g = new graph(n);
        for(int i=0;i<n-1;i++)
        {
            str = (br.readLine()).trim().split(" ");
            int u = Integer.parseInt(str[0]);
            int v = Integer.parseInt(str[1]);
            int type = Integer.parseInt(str[2]);
            if(type == 0)
                g.add(u,v);
        }
        long mod = 1000000000 + 7;
        long sum = 0;
        boolean[] vis = new boolean[n+1];
        //g.print();
        for(int i=1;i<=n;i++)
        {
            long pro = 1;
            if(!vis[i])
            {
                g.count = 0;
                g.dfs(i,vis);
                //System.out.println(g.count);
                for(int j=0;j<k;j++)
                {
                    pro = (pro*g.count)%mod;
                }
                sum = (sum + pro)%mod;
            }    
        }
        long total = 1;
        for(int i=0;i<k;i++)
        {
            total = (total*n)%mod;
        }
        long ans = (total - sum + mod)%mod;
        out.println(ans);
       	out.close();
    }
}
