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.LinkedList;
import java.util.StringTokenizer;

public class CF1139C {
    static LinkedList<Integer> list[];
    static long power(long a, long b) {
        if(b == 0)
            return 1L;

        long val = power(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 dfs(int i,boolean[] visited){
        visited[i] = true;
        count++;
        //System.out.println("Here");
        for(int j : list[i]){
            if(!visited[j]){
                dfs(j,visited);
            }
        }
    }
    static long count = 0L;
    public static void main(String[] args) {
        FastReader input = new FastReader();
        long n = input.nextLong();
        long k = input.nextLong();
        list = new LinkedList[(int)n+1];
        for(int i = 1;i <= n;i++){
            list[i] = new LinkedList<Integer>();
        }
        for(int i = 0;i < n-1;i++){
            int u = input.nextInt();
            int v = input.nextInt();
            int color = input.nextInt();
            if(color == 0){
                list[u].add(v);
                list[v].add(u);
            }
        }
        long res = power(n,k);
        long sub = 0;
        boolean[] visited = new boolean[(int)n+1];
        for(int i = 1;i <= n;i++){
            if(!visited[i]){
                count = 0L;
                dfs(i,visited);
                //System.out.println(count);
                sub += power(count,k);
            }
        }
        sub = sub % mod;
        res = (res - sub + mod) % mod;
        System.out.println(res);
    }
    static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;

        public FastReader()
        {
            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;
        }
    }
}