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.
//Codeforces 548 (Div. 2), 2019_03_21
import java.io.*;
import java.util.*;

public class TaskC {

    public final static int M = 1000000007;

    public static int cnt(int i, ArrayList<ArrayList<Integer>> e, int[] c) {
        int q = 1;
        c[i] = 1;
        for (Integer j : e.get(i)) {
            if (c[j] == 0) {
                q += cnt(j, e, c);
            }
        }
        return q;
    }

    public static int pow(int a, int b) {
        long q = 1;
        long p = a;
        while (b > 0) {
            if ((b & 1) == 1) {
                q = (q*p)%M;
            }
            p = (p*p)%M;
            b >>= 1;
        }
        return (int)q;
    }

    public static void main (String[] args) throws IOException {
        FastScanner fs = new FastScanner(System.in);
        PrintWriter pw = new PrintWriter(new BufferedOutputStream(System.out));

        int n = fs.nextInt();
        int k = fs.nextInt();

        ArrayList<ArrayList<Integer>> e = new ArrayList<ArrayList<Integer>>();
        for (int i = 0; i < n; i++) {
            e.add(new ArrayList<Integer>());
        }

        for (int i = 1; i < n; i++) {
            int u = fs.nextInt() - 1;
            int v = fs.nextInt() - 1;
            int x = fs.nextInt();
            if (x == 0) {
                e.get(u).add(v);
                e.get(v).add(u);
            }
        }

        int[] c = new int[n];
        ArrayList<Integer> q = new ArrayList<Integer>();

        for (int i = 0; i < n; i++) {
            if (c[i] == 0) {
                q.add(cnt(i, e, c));
            }
        }

        long s = 0;
        for (int i = 0; i < q.size(); i++) {
            s = (s + pow(q.get(i), k))%M;
        }

        long ans = (pow(n,k)%M+M-s)%M;
        pw.println(ans);

        pw.close();
    }

    static class FastScanner {
        BufferedReader reader;
        StringTokenizer tokenizer;
        FastScanner(InputStream i) {
            reader = new BufferedReader(new InputStreamReader(i));
            tokenizer = new StringTokenizer("");
        }
        String next() throws IOException {
            while(!tokenizer.hasMoreTokens()) tokenizer = new StringTokenizer(reader.readLine());
            return tokenizer.nextToken();
        }
        int nextInt() throws IOException {
            return Integer.parseInt(next());
        }
    }
}