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 org.omg.PortableInterceptor.SYSTEM_EXCEPTION;

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


// author @mdazmat9
public class codeforces{


    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int test = 1;
        for (int ind = 0; ind < test; ind++) {
            int n=sc.nextInt();
            int k=sc.nextInt();
            Graph g=new Graph(n);

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

                if(col == 0) {
                    g.addEdge(u,v);
                }
            }
            long ans = fast_pow(n, k);
            long rem = g.DFS(k);
           // out.println(ans+" "+rem);
            ans = (ans - rem + mod) % mod;
            out.println(ans);




        }
        out.flush();
    }
    static long fast_pow(long a, long b) {
        if(b == 0)
            return 1L;

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

        if(b % 2 == 0)
            return val * val % mod;
        else
            return val * val % mod * a % mod;
    }
    static long mod = (long)1e9 + 7;
    static   void shuffle(int[] a) {
        int n = a.length;
        for(int i = 0; i < n; i++) {
            int r = i + (int) (Math.random() * (n - i));
            int tmp = a[i];
            a[i] = a[r];
            a[r] = tmp;
        }
    }
    static long gcd(long a , long b)
    {
        if(b == 0)
            return a;
        return gcd(b , a % b);
    }

}
class Scanner {
    public BufferedReader reader;
    public StringTokenizer st;

    public Scanner(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream));
        st = null;
    }

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

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

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

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

class OutputWriter {
    BufferedWriter writer;

    public OutputWriter(OutputStream stream) {
        writer = new BufferedWriter(new OutputStreamWriter(stream));
    }

    public void print(int i) throws IOException {
        writer.write(i);
    }

    public void print(String s) throws IOException {
        writer.write(s);
    }

    public void print(char[] c) throws IOException {
        writer.write(c);
    }

    public void close() throws IOException {
        writer.close();
    }

}
class Pair {
    int x;
    int y;

    // Constructor
    public Pair(int x, int y)
    {
        this.x = x;
        this.y = y;
    }
}
class Compare {

    static void compare(Pair arr[], int n)
    {
        // Comparator to sort the pair according to second element
        Arrays.sort(arr, new Comparator<Pair>() {
            @Override public int compare(Pair p1, Pair p2)
            {
                return p1.x - p2.x;
            }
        });
    }
}

class Graph {
    // A user define class to represent a graph.
    // A graph is an array of adjacency lists.
    // Size of array will be V (number of vertices
    // in graph)
    int V;
    ArrayList<Integer>[] adjListArray;

    // constructor
    Graph(int V) {
        this.V = V;
        // define the size of array as
        // number of vertices
        adjListArray = new ArrayList[V];

        // Create a new list for each vertex
        // such that adjacent nodes can be stored

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

    // Adds an edge to an undirected graph
    void addEdge(int src, int dest) {

        // Add an edge from src to dest.
        //src--;dest--; //do this for 1 based indexing

        //
        adjListArray[src].add(dest);

        // Since graph is undirected, add an edge from dest
        // to src also
          adjListArray[dest].add(src);
    }





    void DFSUtil(int u,boolean[] visited) {
        // Mark the current node as visited and print it
              visited[u] = true;
                count++;
         //   System.out.print(set);

        // Recur for all the vertices adjacent to this vertex
        for (int i = 0; i < adjListArray[u].size(); i++) {
            int n = adjListArray[u].get(i);
            if (!visited[n]) {
                DFSUtil(n, visited);
            }
        }
        // visited[u] = false;

    }
    static long fast_pow(long a, long b) {
        if(b == 0)
            return 1L;

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

        if(b % 2 == 0)
            return val * val % mod;
        else
            return val * val % mod * a % mod;
    }
    static long mod = (long)1e9 + 7;
static long count=0;
    // The function to do DFS traversal. It uses recursive DFSUtil()
    long DFS(int k) {
        // Mark all the vertices as not visited(set as
        // false by default in java)
        boolean visited[] = new boolean[V];
        long rem=0;
        // Call the recursive helper function to print DFS traversal
        for(int i = 0; i < V; ++i) {
            if(!visited[i] ) {
                count = 0;
                DFSUtil(i,visited);
                rem += fast_pow(count, k);
            }
        }
        rem %= mod;
       return rem;
    }
}