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.
//package F;

import java.io.*;
import java.security.KeyPair;
import java.util.*;
import java.math.*;

public class Main {
    static long mod = (long) (1e9 + 7);

    private static long pow(long a, long b) {
        if (b == 0)
            return 1L;

        long val = pow(a, b / 2);

        if (b % 2 == 0)
            return val * val % mod;
        else
            return val * val % mod * a % mod;
    }

    public static void solve() {
        int n = in.nextInt();
        int k = in.nextInt();

        List<Integer>[] graph = new ArrayList[n + 1];

        for (int i = 1; i <= n; i += 1) {
            graph[i] = new ArrayList<>();
        }

        for (int i = 1; i < n; i += 1) {
            int from = in.nextInt();
            int to = in.nextInt();
            int color = in.nextInt();

            if (color == 0) {
                graph[from].add(to);
                graph[to].add(from);
            }
        }

        boolean[] visited = new boolean[n + 1];
        List<Integer> comps = new ArrayList<>();

        for (int i = 1; i <= n; i += 1) {
            if (!visited[i]) {
                comps.add(dfs(i, graph, visited));
            }
        }

        long count = 0;
        for (int c : comps) {
            count = (count +  pow(c, k)%mod) % mod;
        }

        long pow = pow(n, k);
        long ans = ((pow - count) + mod) % mod;
        out.println(ans);
    }

    private static int dfs(int node, List<Integer>[] graph, boolean[] visited) {
        int nodes = 1;
        visited[node] = true;

        for (int n : graph[node]) {
            if (!visited[n])
                nodes += dfs(n, graph, visited);
        }

        return nodes;
    }


    public static InputReader in = new InputReader();
    public static PrintWriter out;

    public static void main(String[] args) {
        out = new PrintWriter(System.out);
        solve();
        out.close();
    }


    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader() {
            reader = new BufferedReader(new InputStreamReader(System.in));
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

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

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

        /**
         * When you call next(), that entire line will be skipped.
         * No flushing buffers.
         * Doesn't work when you want to scan the remaining line.
         *
         * @return entire line
         */
        public String nextLine() {
            String str = "";
            try {
                str = reader.readLine();
                tokenizer = null;
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            return str;
        }
    }
}