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.Arrays;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in Actual solution is at the top
 *
 * @author MaxHeap
 */
public class Main {

  public static void main(String[] args) {
    InputStream inputStream = System.in;
    OutputStream outputStream = System.out;
    InputReader in = new InputReader(inputStream);
    PrintWriter out = new PrintWriter(outputStream);
    CEdgyTrees solver = new CEdgyTrees();
    solver.solve(1, in, out);
    out.close();
  }

  static class CEdgyTrees {

    static final long MOD = (long) (1e9 + 7);

    public void solve(int testNumber, InputReader in, PrintWriter out) {
      int n = in.nextInt();
      int k = in.nextInt();
      DisjointSet ds = new DisjointSet(n);
      int[] size = ArrayUtils.createArray(n, 1);
      for (int i = 0; i < n - 1; ++i) {
        int u = in.nextInt() - 1;
        int v = in.nextInt() - 1;
        boolean isWhite = in.nextInt() == 0;
        if (isWhite) {
          ds.merge(u, v);
        }
      }
      long all = LongMath.powMod(n, k, MOD);
      long other = 0;
      for (int i = 0; i < n; ++i) {
        if (ds.find(i) == i) {
          other = (other + LongMath.powMod(ds.getSize(i), k, MOD)) % MOD;
        }
      }
      all = ((all - other) % MOD + MOD) % MOD;
      out.println(all);
    }

  }

  static class DisjointSet {

    int[] parent;
    int[] rank;
    int[] count;

    public DisjointSet(int[] parent, int[] rank) {
      this.parent = parent.clone();
      this.rank = rank.clone();

    }

    public DisjointSet clone() {
      return new DisjointSet(parent, rank);
    }

    public DisjointSet(int size) {
      parent = new int[size];
      for (int i = 0; i < size; i++) {
        parent[i] = i;
      }
      rank = new int[size];
      count = ArrayUtils.createArray(size, 1);
    }

    public int find(int x) {
      return x == parent[x] ? x : (parent[x] = find(parent[x]));
    }

    public void merge(int a, int b) {
      a = find(a);
      b = find(b);
      if (a == b) {
        return;
      }
      if (rank[a] < rank[b]) {
        parent[a] = b;
        count[b] += count[a];
      } else {
        parent[b] = a;
        count[a] += count[b];
        if (rank[a] == rank[b]) {
          ++rank[a];
        }
      }
    }

    public int getSize(int u) {
      return count[u];
    }

  }

  static interface FastIO {

  }

  static class ArrayUtils {

    public static int[] createArray(int count, int value) {
      int[] array = new int[count];
      Arrays.fill(array, value);
      return array;
    }

  }

  static class InputReader implements FastIO {

    private InputStream stream;
    private static final int DEFAULT_BUFFER_SIZE = 1 << 16;
    private static final int EOF = -1;
    private byte[] buf = new byte[DEFAULT_BUFFER_SIZE];
    private int curChar;
    private int numChars;

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

    public int read() {
      if (this.numChars == EOF) {
        throw new UnknownError();
      } else {
        if (this.curChar >= this.numChars) {
          this.curChar = 0;

          try {
            this.numChars = this.stream.read(this.buf);
          } catch (IOException ex) {
            throw new InputMismatchException();
          }

          if (this.numChars <= 0) {
            return EOF;
          }
        }

        return this.buf[this.curChar++];
      }
    }

    public int nextInt() {
      int c;
      for (c = this.read(); isSpaceChar(c); c = this.read()) {
      }

      byte sgn = 1;
      if (c == 45) {
        sgn = -1;
        c = this.read();
      }

      int res = 0;

      while (c >= 48 && c <= 57) {
        res *= 10;
        res += c - 48;
        c = this.read();
        if (isSpaceChar(c)) {
          return res * sgn;
        }
      }

      throw new InputMismatchException();
    }

    public static boolean isSpaceChar(int c) {
      return c == 32 || c == 10 || c == 13 || c == 9 || c == EOF;
    }

  }

  static class LongMath {

    private LongMath() {
    }

    public static long powMod(long base, int power, long Mod) {
      base %= Mod;
      long res = 1;
      while (power != 0) {
        if ((power & 1) != 0) {
          res = (res * base) % Mod;
        }
        base = (base * base) % Mod;
        power >>= 1;
      }
      return res;
    }

  }
}

