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.ArrayDeque;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class _548C {
	
	static final long mod=1_000_000_007;

	public static void main(String[] args) {
		FastScanner fs=new FastScanner();
		int n=fs.nextInt(), k=fs.nextInt();
		long ways=fastPow(n, k);
		ArrayList<Integer>[] adj=new ArrayList[n];
		for (int i=0; i<n; i++) adj[i]=new ArrayList<>();
		boolean[] seen=new boolean[n];
		ArrayList<Integer> sizes=new ArrayList<>();
		for (int i=1; i<n; i++) {
			int a=fs.nextInt()-1, b=fs.nextInt()-1, c=fs.nextInt();
			if (c==1) continue;
			adj[a].add(b);
			adj[b].add(a);
		}
		for (int base=0; base<n; base++) {
			if (seen[base]) continue;
			ArrayDeque<Integer> bfs=new ArrayDeque<>();
			bfs.add(base);
			seen[base]=true;
			int size=1;
			while (!bfs.isEmpty()) {
				int next=bfs.remove();
				for (int i:adj[next]) {
					if (seen[i])continue;
					seen[i]=true;
					size++;
					bfs.add(i);
				}
			}
			sizes.add(size);
		}
		for (int i:sizes) {
			ways=((ways-fastPow(i, k))%mod+mod)%mod;
		}
		System.out.println(ways);
	}
	
	static long fastPow(int base, int pow) {
		if (pow==0)
			return 1;
		long half=fastPow(base, pow/2);
		if (pow%2==0)
			return half*half%mod;
		return half*half%mod*base%mod;
	}
	
	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		public String next() {
			while (!st.hasMoreElements())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		
		public int nextInt() {
			return Integer.parseInt(next());
		}
	}

}
