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.*;

import static java.util.Optional.ofNullable;

public class C548 {
    static List<List<Endpoint>> edges = new ArrayList<>();
    static Set<Set<Integer>> components = new HashSet<>();
    public final static int BLACK = 1;
    public final static int RED = 0;

    public static void main(String[] args) {
        int n, k;
        Scanner scanner = new Scanner(System.in);
        n = scanner.nextInt();
        k = scanner.nextInt();
        for (int i = 0; i < n; i++){
            edges.add(new ArrayList<>());
        }
        Endpoint first = null;
        for(int i = 0; i < n - 1; i++){
            int u = scanner.nextInt() - 1;
            int v = scanner.nextInt() - 1;
            int col = scanner.nextInt();
            first = new Endpoint(v, col);
            edges.get(u).add(first);
            edges.get(v).add(new Endpoint(u, col));
        }
        HashSet<Integer> component = new HashSet<>();
        component.add(first.getVertex());
        components.add(component);
        dfs(first, -1, component);
        long sum = 0;
        long mod=  1000000007;
        for (Set<Integer> df : components) {
            int size = df.size();
            long tmp = Double.valueOf(Math.pow(size, k)).longValue();
            tmp %= mod;
            sum += tmp;
        }
        sum %= mod;
        double ans = (Math.pow(n, k) % mod - sum % mod) % mod;
        System.out.println(Double.valueOf(ans).longValue());
    }

    private static void dfs(Endpoint v, int parent, Set<Integer> component){
        for (Endpoint endpoint : edges.get(v.getVertex())) {
            if (endpoint.getVertex() == parent)
                continue;
            if (endpoint.getColour() != BLACK){
                component.add(endpoint.getVertex());
                dfs(endpoint, v.getVertex(), component);
            }else {
                HashSet<Integer> set = new HashSet<>();
                set.add(endpoint.getVertex());
                components.add(set);
                dfs(endpoint, v.getVertex(), set);
            }
        }
    }

}

class Endpoint{
    private int vertex;
    private int colour;

    public Endpoint(int vertex, int colour) {
        this.vertex = vertex;
        this.colour = colour;
    }

    public void setVertex(int vertex) {
        this.vertex = vertex;
    }

    public void setColour(int colour) {
        this.colour = colour;
    }

    public int getVertex() {
        return vertex;
    }

    public int getColour() {
        return colour;
    }
}