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.*;
import java.util.*;

public class Main {

    static class Task {
        PrintWriter out;
        MyScanner in;


        private static long MOD = 1_000_000_000 + 7;

        class Edge {
            int to;
            boolean black;

            @Override
            public String toString() {
                return "Edge{" +
                        "to=" + to +
                        ", black=" + black +
                        '}';
            }

            public Edge(int to, boolean black) {
                this.to = to;
                this.black = black;


            }
        }

        List<Edge>[] tree;
        boolean vis[];
        int k;

        public void solve(MyScanner in, PrintWriter out) {
            int n = in.nextInt();
             k = in.nextInt();

            tree = new ArrayList[n];

            long total = pow(n);

            vis = new boolean[n];
            for (int i = 0; i < n; i++) {
                vis[i] = false;
                tree[i] = new ArrayList<>();
            }

            for (int i = 0; i < (n - 1); i++) {
                int u = in.nextInt();
                int v = in.nextInt();
                int bl = in.nextInt();
                u--;
                v--;

                tree[u].add(new Edge(v, bl == 1));
                tree[v].add(new Edge(u, bl == 1));
            }

            long bad = 0;

            for (int i = 0; i < n; i++) {
                //System.out.println("Tree [ " + i + "] = " + tree[i]);
                if (!vis[i]) {
                    int size = count(i);
                    bad = (bad + pow(size)) % MOD;
                   // System.out.println("Found block of size " + size + "  giving " + pow(size));
                }
            }

           // System.out.println("Total " + total + " bad " + bad);
            long good = total - bad;
            while (good < 0) {
                good += MOD;
            }

            out.println(good);

        }

        long pow(int a) {
            long total = 1;
            for (int i = 0; i < k; i++) {
                total = ( total * a) % MOD;
            }
            return total;
        }

        int count(int v) {
            vis[v] = true;

            int sum = 1;


            for (Edge edge: tree[v]) {
                if (!vis[edge.to] && !edge.black) {
                    sum += count(edge.to);
                }
            }

            return sum;

        }

    }

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

    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}