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.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.Queue;
import java.util.Set;

public class Main {
	private static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	private static int mod = 1000000007;
	static long power(long x, long y, int p) 
    { 
        // Initialize result 
        long res = 1;      
         
        // Update x if it is more   
        // than or equal to p 
        x = x % p;  
      
        while (y > 0) 
        { 
            // If y is odd, multiply x 
            // with result 
            if((y & 1)==1) 
                res = (res * x) % p; 
      
            // y must be even now 
            // y = y / 2 
            y = y >> 1;  
            x = (x * x) % p;  
        } 
        return res; 
    } 
	private static int n;
	private static int k;
	private static ArrayList<Integer> gr[];
	private static boolean v[];
	
	private static int dfs(int x) {
		v[x] = true;
		int ans = 1;
		for(int y: gr[x]) {
			if(!v[y]) ans += dfs(y);
		}
		return ans;
	}
	
	public static void main(String[] args) throws NumberFormatException, IOException {
		String s[] = br.readLine().trim().split(" ");
		n = Integer.parseInt(s[0]);
		k = Integer.parseInt(s[1]);
		gr = new ArrayList[n+1];
		for(int i = 1; i <= n; i++) {
			gr[i] = new ArrayList<Integer>();
		}
		v = new boolean[n+1];
		for(int i = 0; i < n-1; i++) {
			s = br.readLine().trim().split(" ");
			if(Integer.parseInt(s[2]) == 0) {
				int x = Integer.parseInt(s[0]);
				int y = Integer.parseInt(s[1]);
				gr[x].add(y);
				gr[y].add(x);
			}
		}
		long ans = 0;
		for(int i = 1; i <= n; i++) {
			if(!v[i]) {
				ans = (ans + power(dfs(i), k, mod))%mod;
			}
		}
		System.out.println((power(n,k,mod)-ans+mod)%mod);
	}
}
