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.util.ArrayList;
import java.util.LinkedList;

/**
 * Created by himanshubhardwaj on 09/04/19.
 */
public class EdgyTrees {
    static long mod = 1000000007;

    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String[] str = br.readLine().split(" ");

        int n = Integer.parseInt(str[0]);
        int k = Integer.parseInt(str[1]);

        Tree tree = new Tree(n);

        for (int i = 0; i < (n - 1); i++) {
            str = br.readLine().split(" ");
            int source = Integer.parseInt(str[0]) - 1;
            int destination = Integer.parseInt(str[1]) - 1;
            boolean isGood = (Integer.parseInt(str[2]) == 1) ? false : true;
            tree.insert(source, destination, isGood);
        }
        long sum = 0;
        for (int x : tree.connectedComponents(n)) {
          //  System.out.print(x+", ");
            sum += powMod(x, k);
            sum = sum % mod;
        }
        //System.out.println("------");
        //System.out.println(tree.count);


        System.out.print((powMod(n, k) - sum+mod) % mod);

    }


    static long powMod(long a, long x) {
        long temp = 1;
        for (int i = 1; i <= x; i++) {
            temp = (temp * a) % mod;
        }
        return temp;
    }
}


class Tree {
    ArrayList<Integer>[] neighbours = null;
    int count = 0;


    public Tree(int n) {
        neighbours = new ArrayList[n];

        for (int i = 0; i < n; i++) {
            neighbours[i] = new ArrayList<>();
        }
    }


    void insert(int source, int destination, boolean isGood) {
        if (isGood) {
            neighbours[source].add(destination);
            neighbours[destination].add(source);
            count++;
        }
    }

    ArrayList<Integer> connectedComponents(int n) {
        boolean[] reached = new boolean[n];
        ArrayList<Integer> connectedComponentSize = new ArrayList<>();

        for (int i = 0; i < n; i++) {
            if (!reached[i]) {
                connectedComponentSize.add(connectedComponentSize(i, -1, reached));
            }
        }


        return connectedComponentSize;
    }

    private Integer connectedComponentSize(int node, int parent, boolean[] reached) {
        if (reached[node]) {
            return 0;
        }

        reached[node] = true;
        int count = 1;

        for (int neightbour : neighbours[node]) {
            if (neightbour != parent) {
                count += connectedComponentSize(neightbour, node, reached);
            }
        }
        return count;
    }
}