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 Sol {

	static final boolean stdin = true;
	static final String filename = "";
	static FastScanner br;
	static PrintWriter pw;

	public static void main(String[] args) throws IOException {

		if (stdin) {
			br = new FastScanner();
			pw = new PrintWriter(new OutputStreamWriter(System.out));
		} else {
			br = new FastScanner(filename + ".in");
			pw = new PrintWriter(new FileWriter(filename + ".out"));
		}

		Solver solver = new Solver();
		solver.solve(br, pw);
	}

	static class Solver {
		static ArrayList<Integer>[] adj;
		static boolean[] vis;
		public void solve(FastScanner br, PrintWriter pw) throws IOException {
			int nodes = br.nextInt(), k = br.nextInt();
			adj = new ArrayList[nodes];
			for (int i = 0; i < nodes; i++) {
				adj[i] = new ArrayList<Integer>();
			}
			for (int i = 0; i < nodes-1; i++) {
				int a = br.nextInt() - 1;
				int b = br.nextInt() - 1;
				if(br.nextInt() == 0){
					adj[a].add(b);
					adj[b].add(a);
				}
			}
			vis = new boolean[nodes];
			Arrays.fill(vis, false);
			long out = (long) Math.pow(nodes, k);
			for(int i = 0; i < nodes; i++){
				long cnt = deefus(i);
				out -= Math.pow(cnt, k);
				if(out < 0){
					out += 1000000007;
				}
			}
			
			pw.println(out % 1000000007);
			pw.close();
		}
		
		public static long deefus(int node){
			long out = 1;
			if(vis[node])
				out--;
			vis[node] = true;
			for(int i : adj[node]){
				if(!vis[i]){
					out+=deefus(i);
				}
			}
			return out;
		}

	}

	static class Point implements Comparable<Point> {
		int a;
		int b;

		Point(int a, int b) {
			this.a = a;
			this.b = b;
		}

		@Override
		public int compareTo(Point o) {
			return this.a - o.a;
		}

	}

	static class Dsu {
		int n;
		int[] parent;
		int[] rank;

		public Dsu(int n) {
			this.n = n;
			parent = new int[n];
			rank = new int[n];
		}

		public void createSet() {
			for (int i = 0; i < n; i++) {
				parent[i] = i;
				rank[i] = 0;
			}
		}

		public int findParent(int x) {
			if (parent[x] == x)
				return x;
			parent[x] = findParent(parent[x]);
			return parent[x];
		}

		public void mergeSet(int a, int b) {
			int pa = findParent(a);
			int pb = findParent(b);

			if (pa == pb)
				return;

			if (rank[pa] > rank[pb]) {
				parent[pb] = pa;
			} else if (rank[pa] < rank[pb]) {
				parent[pa] = pb;
			} else {
				parent[pb] = pa;
				rank[pa]++;
			}
		}
	}

	public static class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		public FastScanner(String s) {
			try {
				br = new BufferedReader(new FileReader(s));
			} catch (FileNotFoundException e) {
				e.printStackTrace();
			}
		}

		public FastScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String nextToken() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(nextToken());
		}

		long nextLong() {
			return Long.parseLong(nextToken());
		}

		double nextDouble() {
			return Double.parseDouble(nextToken());
		}

		ArrayList<Integer>[] nextGraph(int nodes, int edges) {
			ArrayList<Integer>[] adj = new ArrayList[nodes];
			for (int i = 0; i < nodes; i++) {
				adj[i] = new ArrayList<Integer>();
			}
			for (int i = 0; i < edges; i++) {
				int a = nextInt() - 1;
				int b = nextInt() - 1;
				adj[a].add(b);
				adj[b].add(a);
			}
			return adj;
		}
	}
}