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 AiseHi {
	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; 
        } 
    }
	static FastReader sc = new FastReader();
	static int mod = (int)(1e9+7);
	public static void main (String[] args) {
		PrintWriter out = new PrintWriter(System.out);
		int t = 1;
//    	t = sc.nextInt();
    	while(t-->0) {
    		int n = sc.nextInt();
    		int k = sc.nextInt();
    		DSU dsu = new DSU(n+1);
    		Arrays.fill(dsu.par, -1);
    		for(int i=1;i<n;i++) {
    			int u = sc.nextInt();
    			int v = sc.nextInt();
    			int x = sc.nextInt();
    			if(x == 0) {
    				if(dsu.par[u] == -1) dsu.par[u] = u;
    				if(dsu.par[v] == -1) dsu.par[v] = v;
    				dsu.join(u, v);
    			}
    		}
    		long total = pow(n,k) % mod;
//    		out.write(total+"\n");
    		long bad = 0;
//    		for(int i=1;i<=n;i++)
//    			out.write(dsu.par[i]+" "+dsu.size[i]+"\n");
//    		out.write("\n");
    		for(int i=1;i<=n;i++) {
    			if(dsu.par[i] == -1)
    				bad = (bad+1)%mod;
    			if(dsu.par[i] == i)
    				bad = (bad%mod + pow(dsu.size[i],k)%mod)%mod;
    		}
//    		out.write(bad+"\n");
    		total = (total%mod - bad%mod + mod)%mod;
    		out.write(total+"\n");
      	}
		out.close();
	}
	private static long pow(long i, long x) {
		long ans = 1;
		while(x>0) {
			if(x%2==0) {
				i = (i%mod *i%mod)%mod;
				x = x/2;
			}
			else {
				ans = (ans%mod * i%mod)%mod;
				x--;
			}
		}
		return ans%mod;
	}
	private static void swap(int[] a, int i, int j) {
		int temp = a[i];
		a[i] = a[j];
		a[j] = temp;
	}
	static long lstbt(long val) {
		long msk = val & (val-1);
		return (long) (Math.log(val^msk)/Math.log(2));
	}
	private static long sqrt(long x) {
		long l = 1,h = x;
		long ans = 0;
		while(l<=h) {
			long mid = (l+(h-l)/2);
			if(mid>x/mid) h = mid-1;
			else {
				ans = mid;
				l = mid+1;
			}
		}
		return ans;
	}
//	static boolean prime[] = new boolean[10000001];
//	static void sieve() {
//		prime[0] = true;
//		prime[1] = true;
//		int max = 10000000;
//		for(int i=2;i*i<=max;i++) {
//			if(!prime[i]) {
//				for(int j=i*i;j<=max;j+=i)
//					prime[j] = true;
//			}
//		}
//	}
}
class DSU {
	int par[];
	int size[];
	DSU(int n) {
		par = new int[n];
		size = new int[n];
		Arrays.fill(size, 1);
		for(int i=0;i<n;i++) par[i] = i;
	}
	int findPar(int x) {
		if(x == par[x]) return x;
		
		return par[x] = findPar(par[x]);
	}
	boolean join(int u,int v) {
		int fu = findPar(u);
		int fv = findPar(v);
		if(fu!=fv) {
			if(size[fu]>=size[fv]) {
				par[fv] = fu;
				size[fu] += size[fv];
			}
			else {
				par[fu] = fv;
				size[fv] += size[fu];
			}
			return true;
		}
		else 
			return false;
	}
}
class pair implements Comparable<pair>{
	int a;
	long b;
	pair(int a,long b){
		this.a = a;
		this.b = b;
	}
	@Override
	public int compareTo(pair o) {
		if(this.a!=o.a)
			return (int) (this.a - o.a);
		else
			return (int)(this.b - o.b);
	}
}