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

public class c
{
    static long mod = (long)1e9+7;
    
    public static void main(String[] args) throws IOException
    {
        FastScanner in = new FastScanner(System.in);
        int n = in.nextInt();
        int k = in.nextInt();
        DSU tree = new DSU(n);
        for (int i = 0; i < n-1; i++)
        {
            int u = in.nextInt()-1;
            int v = in.nextInt()-1;
            int x = in.nextInt();
            if (x == 1) continue;
            tree.union(u, v);
        }
        
        int[] sizes = new int[n];
        for (int i = 0; i < n; i++)
            sizes[tree.find(i)]++;
        long ans = exp(n, k);
        for (int i = 0; i < n; i++)
        {
            ans -= exp(sizes[i], k);
            if (ans < 0) ans += mod;
        }
        ans %= mod;
        System.out.println(ans);
    }
    
    public static long exp(long s, long k)
    {
        if (s == 0) return 0;
        if (k == 0) return 1L;
        if (k == 1) return s %mod;
        long ans = exp(s, k/2);
        ans *= ans; ans %= mod;
        if (k %2 == 0) return ans;
        return (s*ans) %mod;
    }
    
    public static class DSU
    {
        int[] set;
        
        DSU(int n)
        {
            Arrays.fill(set = new int[n], -1);
        }
        
        int find(int i)
        {
            return set[i] < 0 ? i : (set[i] = find(set[i]));
        }
        
        boolean union(int a, int b)
        {
            if ((a = find(a)) == (b = find(b))) return false;
            if (set[a] == set[b]) set[a]--;
            if (set[a] <= set[b]) set[b] = a; else set[a] = b;
            return true;
        }
    }
    
    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;
    	
        public FastScanner(InputStream i) {
            br = new BufferedReader(new InputStreamReader(i));
            st = new StringTokenizer("");
        }
    			
        public String next() throws IOException {
            if(st.hasMoreTokens())
                return st.nextToken();
            else
                st = new StringTokenizer(br.readLine());
            return next();
        }
    
        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }
        //$
    }
    
}