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.
//I AM THE CREED
/* //I AM THE CREED
/* package codechef; // don't place package name! */
import java.io.BufferedReader; 
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.util.StringTokenizer; 
import java.util.*;
import java.awt.Point;
public class Main{
    static long mod=1000000007;
    public static void main(String[] args) throws IOException 
    { 
        Scanner input=new Scanner(System.in);
        while(input.hasNext()){
            int n=input.nextInt();
            long k=input.nextLong();
            ArrayList<ArrayList<Integer>> graph=new ArrayList<>();
            HashMap<String, Integer> col=new HashMap<>();
            HashSet<Integer> visited=new HashSet<>();
            long ways=0;
            for(int i=0;i<=n;i++){
                graph.add(new ArrayList<>());
            }
            
            for(int i=0;i<n-1;i++){
                int u=input.nextInt();
                int v=input.nextInt();
                int color=input.nextInt();
                graph.get(u).add(v);
                graph.get(v).add(u);
                col.put(Integer.toString(u)+","+Integer.toString(v), color);
                col.put(Integer.toString(v)+","+Integer.toString(u), color);
            }
            for(int i=1;i<=n;i++){
                if(visited.contains(i)){
                    continue;
                }
                long vertices=dfs(graph, visited, i, col);
                ways=(ways+((pow(vertices, k))-vertices+mod)%mod)%mod;
            }
            System.out.println((pow((long)(n), k)-ways-n+mod+mod)%mod);
        }
        
    }
    static long pow(long a, long b){
        if(b==1){
            return a%mod;
        }
        return (pow(a, b-1)*a)%mod;
    }
    static long dfs(ArrayList<ArrayList<Integer>> g, HashSet<Integer> v, int n, HashMap<String, Integer> col){
        if(v.contains(n)){
            return (long)(0);
        }
        long tot=1;
        v.add(n);
        for(int children:g.get(n)){
            if(col.get(Integer.toString(n)+","+Integer.toString(children))==1){
                continue;
            }
            tot+=dfs(g, v, children, col);
        }
        return tot;
    }
    //Credits to SecondThread(https://codeforces.com/profile/SecondThread) for this tempelate
    static void ruffle_sort(long[] a) {
		// shandom_ruffle
		Random r=new Random();
		int n=a.length;
		for (int i=0; i<n; i++) {
			int oi=r.nextInt(i);
			long temp=a[i];
			a[i]=a[oi];
			a[oi]=temp;
		}
 
		// sort
		Arrays.sort(a);
	}
    //Credits to SecondThread(https://codeforces.com/profile/SecondThread) for this tempelate.
    static class FastScanner {
		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) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}
	}
    
    
}