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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Set;
import java.util.Stack;

public class JavaApplication6 {

    static PrintWriter out = new PrintWriter(System.out);
    static long x = 1000000007;

    public static void main(String[] args) throws IOException {

        BufferedReader input = new BufferedReader(new InputStreamReader(System.in));
        int[] tab = parseArray(input);
        int n = tab[0];
        int m = tab[1];
        long sum = 0;
        long result = 1;
        boolean[] find = new boolean[n + 1];
        disjointset ds = new disjointset(n + 1);
        for (int k = 0; k < n - 1; k++) {
            tab = parseArray(input);
            if (tab[2] == 0) {
                ds.unify(tab[0], tab[1]);
            }
        }
        ArrayList<Integer> set = new ArrayList<>();

        Arrays.fill(find, false);
        for (int k = 1; k <= n; k++) {
            if (!find[ds.find(k)] && ds.componentSize(k) != 1) {

                set.add(ds.componentSize(k));
                find[ds.find(k)] = true;
            }
        }

        for (int e : set) {
            long temp = 1;
            for (int k = 0; k < m; k++) {
                temp *= e;
                temp %= x;
            }
            temp = (temp - e + x) % x;
            sum += temp;
            sum %= x;
        }

        for (int k = 0; k < m; k++) {
            result *= n;
            result %= x;
        }
        result = (result - n + x) % x;
        result = (result - sum + x) % x;
        out.println(result);
        out.close();
    }

    static int[] parseArray(BufferedReader gi) throws IOException {
        String[] line = gi.readLine().trim().split(" ");
        int[] rez = new int[line.length];
        for (int k = 0; k < line.length; k++) {
            rez[k] = Integer.parseInt(line[k]);
        }
        return rez;
    }

}

class disjointset {

    private int size;
    private int[] component;
    private int[] id;
    private int nc;

    public disjointset(int size) {

        if (size <= 0) {
            throw new IllegalArgumentException("error size ");
        }

        this.size = nc = size;
        component = new int[size];
        id = new int[size];

        for (int i = 0; i < size; i++) {
            id[i] = i;
            component[i] = 1;
        }

    }

    public int find(int p) {

        int root = p;
        while (root != id[root]) {
            root = id[root];
        }
        while (p != root) {
            int next = id[p];
            id[p] = root;
            p = next;
        }

        return root;

    }

    

    public int componentSize(int p) {
        return component[find(p)];
    }

    

    public void unify(int p, int q) {
        int r1 = find(p);
        int r2 = find(q);
        if (r1 == r2) {
            return;
        }
        if (component[r1] < component[r2]) {
            component[r2] += component[r1];
            id[r1] = r2;
        } else {
            component[r1] += component[r2];
            id[r2] = r1;
        }
        nc--;
    }

}
