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.StringTokenizer;

public class realC {

	static final int mod = 1_000_000_007;
	
	public static void main(String[] args) {
		FastReader scan = new FastReader();
		int n = scan.nextInt(), k = scan.nextInt();
		DSU set = new DSU(n);
		boolean[] seen = new boolean[n];
		long total = power(n,k,mod);
		for(int i = 0; i < n-1; i++) {
			int a = scan.nextInt()-1, b = scan.nextInt()-1, c = scan.nextInt();
			if(c==0) set.union(a,b);
		}
		for(int i = 0; i < n; i++) {
			int p = set.findParent(i);
			if(seen[p]) continue;
			seen[p] = true;
			long now = power(set.height[p],k,mod);
			total = (total - now + mod) % mod;
		}
		System.out.println(total);
	}

	static long power(int x, int y, int p) {
		long res = 1;
		x = x % p;
		while (y > 0) {
			if ((y & 1) == 1)
				res = ((res%p) * (x%p)) % p;
			y = y >> 1;
			x = ((x%p) * (x%p)) % p;
		}
		return res;
	}

	static class DSU {
		int[] root;
		int[] height;
		int n;

		DSU(int n) {
			this.n = n;
			root = new int[n];
			height = new int[n];
			for (int i = 0; i < n; i++) {
				root[i] = i;
				height[i] = 1;
			}
		}

		int findParent(int i) {
			while(root[i]!=i) {
				root[i] = root[root[i]];
				i=root[i];
			}
			return i;
		}

		boolean union(int x, int y) {
			int parX = findParent(x);
			int parY = findParent(y);
			if (parX == parY)
				return false;
			if (height[parX] < height[parY]) {
				root[parY] = parX;
				height[parX] += height[parY] + 1;
			} else {
				root[parX] = parY;
				height[parY] += height[parX] + 1;
			}
			return true;
		}
	}

	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;
		}
	}

}
