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.HashSet;
import java.util.StringTokenizer;

public class C {
    public static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

    public static void main(String[] args) {
        OutputStreamWriter outputStreamWriter = new OutputStreamWriter(System.out);
        PrintWriter out = new PrintWriter(outputStreamWriter);
        FastReader in = new FastReader();

        int t = 1;
        while (t-- > 0)
            run(in, out);

        out.close();

    }
    static long mod = (long)(1e9+7);
    static long power(long x, long y, long p)
    {
        long res = 1;
        x = x % p;
        while (y > 0)
        {
            if((y & 1)==1)
                res = (res * x) % p;
            y = y >> 1;
            x = (x * x) % p;
        }
        return res;
    }

    private static void run(FastReader in, PrintWriter out) {
        int n = in.nextInt();
        int k = in.nextInt();
        HashSet<Integer> one = new HashSet<>();
        HashSet<Integer> zero = new HashSet<>();
        for (int i = 0; i < n-1; i++) {
            int a = in.nextInt();
            int b = in.nextInt();
            int c = in.nextInt();
            if(c == 0){
                zero.add(a);
                zero.add(b);
            }
            else {
                one.add(a);
                one.add(b);
            }

        }
        if(one.size() == 0){
            out.println(0);
            return;
        }
        long all = power(n,k,mod);
        long etc = power(zero.size(),k,mod);
        int common = 0;
        for (Integer a : zero) {
            if(one.contains(a))
                common++;
        }
        long zz = 0;
        if(common>0)
         zz = power(common-1,k,mod);

        long ans = all - etc - (n - zero.size()) + zz;
        out.println(ans);

    }

}
