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.awt.Point;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigDecimal;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashSet;
import java.util.Hashtable;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Stack;
import java.util.StringTokenizer;


public class N1139C {
	static PrintWriter out;
	static Scanner sc;
	static ArrayList<Integer>ans,w;
	static ArrayList<Point>adj[];
	static HashSet<Integer>primesH;
	static boolean can;
	//static ArrayList<Integer>a;
	static HashSet<Long>h,tmp;
	static boolean[]vis;
	static int[]a,b,c,d,col,dist;
	static int[][]g;
	static long[]l,dp;
	static char[][]mp;
	static long oo=(long)1e9+7;
	public static void main(String[]args) throws IOException {
		sc=new Scanner(System.in);
		out=new PrintWriter(System.out);
		int n=ni(),k=ni();
		int x,y,w;
		adj=new ArrayList[n];
		vis=new boolean[n];

		for(int i=0;i<n;i++)adj[i]=new ArrayList<Point>();
	//	g=new int[n][n];
		for(int i=0;i<n-1;i++) {
			x=sc.nextInt()-1;
			y=sc.nextInt()-1;
			w=sc.nextInt();
			adj[y].add(new Point(x,w));
			adj[x].add(new Point(y,w));
		}
		ans=new ArrayList<Integer>();
		long res=pow(n,k);
		for(int i=0;i<n;i++) {
			if(!vis[i]) {
				long cur=dfs(i);
				long pow=pow(cur,k);
				res=(res-pow%oo+oo)%oo;
//				if(res<0) {
//					res=(res+oo)%oo;
//				}
			}
		}
		
		out.println(res);
		
		out.close();
	}


	private static long pow(long a, long b) {
		if(b==0)return 1;
		long sq=pow(a,b/2)%oo;
		sq=(sq*sq)%oo;
		if(b%2==1) {
			sq=(sq*a)%oo;
		}
		return sq%oo;
	}


	private static int dfs(int u) {
		vis[u]=true;
		int ans=1;
		for(Point p:adj[u]) {
			if(!vis[p.x]&&p.y==0) {
				ans+=dfs(p.x);
			}
		}
	    return ans;
	}

	private static void disp(int[] revl) {
		for(int i=0;i<revl.length;i++) {
			out.print(revl[i]+" ");
		}
		out.println();
	}
	static class Pair implements Comparable<Pair>{
		int a,b;
		Pair(int a,int b){
			this.a=a;
			this.b=b;
		}
		@Override
		public int compareTo(Pair p) {
			return a-p.a;
		}
		public String toString() {
			return "("+a+" "+b+")";
		}
	}
	static int ni() throws IOException {
		return sc.nextInt();
	}
	static double nd() throws IOException {
		return sc.nextDouble();
	}
	static long nl() throws IOException {
		return  sc.nextLong();
	}
	static String ns() throws IOException {
		return sc.next();
	}
	static int[] nai(int n) throws IOException {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = sc.nextInt();
		return a;
	}
	static long[] nal(int n) throws IOException {
		long[] a = new long[n];
		for (int i = 0; i < n; i++)
			a[i] = sc.nextLong();
		return a;
	}
	static int[][] nmi(int n,int m) throws IOException{
		int[][]a=new int[n][m];
		for(int i=0;i<n;i++) {
			for(int j=0;j<m;j++) {
				a[i][j]=sc.nextInt();
			}
		}
		return a;
	}

	static long[][] nml(int n,int m) throws IOException{
		long[][]a=new long[n][m];
		for(int i=0;i<n;i++) {
			for(int j=0;j<m;j++) {
				a[i][j]=sc.nextLong();
			}
		}
		return a;
	}
	static void o(String x) {
		out.print(x);
	}
	static void ol(String x) {
		out.println(x);
	}
	static void ol(int x) {
		out.println(x);
	}
	static class Scanner 
	{
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s){	br = new BufferedReader(new InputStreamReader(s));}

		public String next() throws IOException 
		{
			while (st == null || !st.hasMoreTokens()) 
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
		public boolean hasNext() {return st.hasMoreTokens();}
		public int nextInt() throws IOException {return Integer.parseInt(next());}
		
		public double nextDouble() throws IOException {return Double.parseDouble(next());}
		
		public long nextLong() throws IOException {return Long.parseLong(next());}

		public String nextLine() throws IOException {return br.readLine();}
			
		public boolean ready() throws IOException {return br.ready(); }
		

	}
}
