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.io.IOException;
import java.io.InputStream;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.NoSuchElementException;

public class Main {
    private static FastScanner sc = new FastScanner();
    static Node[] V;
    static long clusterSize = 0;
    private static long mod = 1000000007;

    public static void main(String[] args) {
    	int n = sc.nextInt();
    	int k = sc.nextInt();
    	V = new Node[n];
    	for(int i=0; i<n; i++) {
    		V[i] = new Node();
    	}
    	for(int i=0; i<n-1; i++) {
    		int a = sc.nextInt() - 1;
    		int b = sc.nextInt() - 1;
    		int x = sc.nextInt();
    		if(x == 1) continue;
    		V[a].nbr.add(b);
    		V[b].nbr.add(a);
    	}
    	ArrayList<Long> redCluster = new ArrayList<>();
    	for(int i=0; i<n; i++) {
    		if(!V[i].vst) {
    			clusterSize = 0;
    			V[i].dfs();
    			redCluster.add(clusterSize);
    		}
    	}
    	long ans = power(n, k);
    	for(long x : redCluster) {
    		ans = (ans - power(x, k) + mod) % mod;
    	}
    	System.out.println(ans);
    }

    static class Node {
        HashSet<Integer> nbr = new HashSet<>();
        boolean vst = false;
        void dfs() {
        	vst = true;
        	clusterSize++;
        	for(int x : nbr) {
        		if(!V[x].vst) V[x].dfs();
        	}
        }
    }

    static long power(long m , long n){
    	if(n == 0) {
    		return 1;
    	}else if(n == 1){
            return m;
        }else if(n % 2 == 0){
            long s = power(m, n/2);
            return ( (s % mod) * (s % mod) ) % mod;
        }else{
            return ( (m % mod) * (power(m, n-1) % mod) ) % mod;
        }
    }

    static class FastScanner {
        private final InputStream in = System.in;
        private final byte[] buffer = new byte[1024];
        private int ptr = 0;
        private int buflen = 0;
        private boolean hasNextByte() {
            if(ptr < buflen) {
                return true;
            } else {
                ptr = 0;
                try {
                    buflen = in.read(buffer);
                } catch(IOException e) {
                    e.printStackTrace();
                }
                if(buflen <= 0) {
                    return false;
                }
            }
            return true;
        }
        private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
        private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
        private void skipUnprintable() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;}
        public boolean hasNext() { skipUnprintable(); return hasNextByte();}
        public String next() {
            if (!hasNext()) throw new NoSuchElementException();
            StringBuilder sb = new StringBuilder();
            int b = readByte();
            while(isPrintableChar(b)) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }
        public long nextLong() {
            return Long.parseLong(next());
        }
        public int nextInt(){
            return Integer.parseInt(next());
        }
        public double nextDouble(){
            return Double.parseDouble(next());
        }
    }
}
