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.util.Map.Entry;
import java.lang.*;
import java.io.*;
import java.math.BigInteger;


public class CF {
	private static FS sc = new FS();
	
	private static class FS {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());				               
	            } catch (IOException e) {}
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		long nextLong() {
			return Long.parseLong(next());
		}
	}
	
	private static class extra {
		
		static int[] intArr(int size) {
			int[] a = new int[size];
			for(int i = 0; i < size; i++) a[i] = sc.nextInt();
			return a;
		}
		
		static long[] longArr(int size) {
			long[] a = new long[size];
			for(int i = 0; i < size; i++) a[i] = sc.nextLong();
			return a;
		}
		
		static long intSum(int[] a) {
			long sum = 0; 
			for(int i = 0; i < a.length; i++) {
				sum += a[i];
			}
			return sum;
		}
		
		static long longSum(long[] a) {
			long sum = 0; 
			for(int i = 0; i < a.length; i++) {
				sum += a[i];
			}
			return sum;
		}
		
		static LinkedList[] graphD(int vertices, int edges) {
			LinkedList<Integer>[] temp = new LinkedList[vertices+1];
			for(int i = 0; i <= vertices; i++) temp[i] = new LinkedList<>();
			for(int i = 0; i < edges; i++) {
				int x = sc.nextInt();
				int y = sc.nextInt();
				temp[x].add(y);
			}
			return temp;
		}
		
		static LinkedList[] graphUD(int vertices, int edges) {
			LinkedList<Integer>[] temp = new LinkedList[vertices+1];
			for(int i = 0; i <= vertices; i++) temp[i] = new LinkedList<>();
			for(int i = 0; i < edges; i++) {
				int x = sc.nextInt();
				int y = sc.nextInt();
				temp[x].add(y);
				temp[y].add(x);
			}
			return temp;
		}
		
		static void printG(LinkedList[] temp) {
			for(LinkedList<Integer> aa:temp) System.out.println(aa);
		}
		
		static long cal(long val, long pow) {
			if(pow == 0) return 1;
			long res = cal(val, pow/2);
			
			long ret = (res*res)%mod;
			if(pow%2 == 0) return ret;
			return (val*ret)%mod;
		}
		
		static long gcd(long a, long b) { return b == 0 ? a:gcd(b, a%b); }
		
	}
	
	static int mod = (int)Math.pow(10, 9) + 7;
	static int max = (int) 1e5 + 5;
	static LinkedList<Integer>[] temp;
	static long ans;
	
	public static void main(String[] args) {
//		int t = sc.nextInt();
		int t = 1;
		StringBuilder ret = new StringBuilder();
		while(t-- > 0) {
			int n = sc.nextInt();
			int m = sc.nextInt();
			temp = new LinkedList[n+1];
			for(int i = 0; i <= n; i++) temp[i] = new LinkedList<>();
			for(int i = 1; i < n; i++) {
				int a = sc.nextInt();
				int b = sc.nextInt();
				int col = sc.nextInt();
				if(col == 0) {
					temp[a].add(b);
					temp[b].add(a);
				}
			}
			long fin = 0;
			boolean[] vis = new boolean[n+1];
			for(int i = 1; i <= n; i++) {
				if(!vis[i]) {
					ans = 0;
					dfs(i, vis);
					fin += extra.cal(ans, m)%mod;
				}
			}
			fin = (extra.cal(n, m) - fin + mod)%mod;
			ret.append(fin + "\n");
 		}
		System.out.println(ret);	
	}
	
	static void dfs(int s, boolean[] vis) {
		vis[s] = true;
		ans++;
		for(int aa:temp[s]) {
			if(!vis[aa]) dfs(aa, vis);
		}
	}
	
}