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.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class C1139 {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int N = in.nextInt();
        int K = in.nextInt();
        long mod = 1000000007;
        long all = modPow(N, K, mod);
        Node[] nodes = new Node[N];
        for (int n=0; n<N; n++) {
            nodes[n] = new Node();
        }
        for (int n=1; n<N; n++) {
            int u = in.nextInt()-1;
            int v = in.nextInt()-1;
            int color = in.nextInt();
            if (color == 0) {
                Node nodeu = nodes[u];
                Node nodev = nodes[v];
                nodeu.next.add(nodev);
                nodev.next.add(nodeu);
            }
        }
        long bad = 0;
        for (Node node : nodes) {
            if (!node.seen) {
                int count = visit(node);
                bad += modPow(count, K, mod);
            }
        }
        long good = (all + (mod-bad))%mod;
        System.out.println(good);
    }

    static int visit(Node node) {
        node.seen = true;
        int result = 1;
        for (Node next : node.next) {
            if (!next.seen) {
                result += visit(next);
            }
        }
        return result;
    }

    static long modPow(long base, int exp, long mod) {
        long result = 1;
        for (int i=0; i<exp; i++) {
            result *= base;
            result %= mod;
        }
        return result;
    }

    static class Node {
        boolean seen;
        List<Node> next = new ArrayList<>();
    }

}
