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.lang.*;
    import java.io.*;
    public class C{

    	static long MOD = 1000000007;
        public static int dfs(int u,boolean visited[],ArrayList<Integer> list[]){
        	int count =0;
        	for(int neighbour : list[u]){
        		if(!visited[neighbour]){
        			visited[neighbour] =true;
        			count += dfs(neighbour,visited,list);
        		}
        	}
        	return 1 + count;
        }

        public static long pow(int a,int b){
		    long x =a,y=b;
		    long res = 1;
		    while (y > 0) 
		    { 
		        // If y is odd, multiply x with result 
		        if (y %2!=0) 
		            res = (res*x)%MOD; 

		        y = y>>1; // y = y/2 
		        x = (x*x)%MOD;  // Change x to x^2 
		    } 
		    return res%MOD; 
		}

        public static long f(long count,int connected,int k){
        	return count = (count +pow(connected,k))%MOD;
        }

        public static void main(String[] args){
            InputStream inputStream = System.in;
            InputReader in = new InputReader(inputStream);
            int n = in.nextInt();
            int k = in.nextInt();
            ArrayList<Integer> list[] = new ArrayList[n+1];
            for(int i=1;i<=n;i++)
            	list[i] = new ArrayList<Integer>();
            for(int i=0;i<n-1;i++){
            	int u = in.nextInt();
            	int v = in.nextInt();
            	int x = in.nextInt();
            	if(x==0){
            		list[u].add(v);
            		list[v].add(u);
            	}
            }
            //perform dfs:
            long count = 0;
            boolean visited[] = new boolean[n+1];
            for(int u=1;u<=n;u++){
            	int connected = 0;
            	if(!visited[u]){
            		visited[u] = true;
            		connected = dfs(u,visited,list);
            	}
            	// System.out.println(connected);
            	count = f(count,connected,k);
            }
            count = (pow(n,k) - count)%MOD;
            if(count<0)
            	count += MOD;
            System.out.println(count);
        }

        static class InputReader {
            public BufferedReader reader;
            public StringTokenizer tokenizer;

            public InputReader(InputStream stream) {
                reader = new BufferedReader(new InputStreamReader(stream), 32768);
                tokenizer = null;
            }

            public String next() {
                while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                    try {
                        tokenizer = new StringTokenizer(reader.readLine());
                    } catch (IOException e) {
                        throw new RuntimeException(e);
                    }
                }
                return tokenizer.nextToken();
            }

            public long nextLong() {
                return Long.parseLong(next());
            }
            public int nextInt() {
                return Integer.parseInt(next());
            }
        }
    }