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. 

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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 Main {
    static int n, k;
    static ArrayDeque[] edges;
    static boolean[] seen;
    static long mod = (long)(1e9 + 7);
	public static void main (String[] args) throws IOException {
	    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	    String[] line = br.readLine().split(" ");
	    n = p(line[0]);
	    k = p(line[1]);
	    edges = new ArrayDeque[n];
	    for(int i = 0; i < n; ++i) edges[i] = new ArrayDeque<>();
	    
	    for(int i = 0; i < n - 1; ++i){
	        line = br.readLine().split(" ");
	        int a = p(line[0]) - 1, b = p(line[1]) - 1, c = p(line[2]);
	        edges[a].offer(new edge(b, c));
	        edges[b].offer(new edge(a, c));
	    }
	    
	    long tot = pow(n, k);
	    seen = new boolean[n];
	    for(int i = 0; i < n; ++i){
	        if(!seen[i]){
	            int size = dfs(i);
	            long num = pow(size, k);
	            tot = (tot - num + mod) % mod;
	        }
	    }
	    
	    System.out.println(tot);
	}
	static int dfs(int idx){
	    seen[idx] = true;
	    int out = 1;
	    for(edge e : (ArrayDeque<edge>) edges[idx]){
	        if(!seen[e.v] && e.c == 0){
	            out += dfs(e.v);
	        }
	    }
	    return out;
	}
	static long pow(long base, int pow){
	    if(pow == 0) return 1;
	    if(pow == 1) return base;
	    long out = pow(base, pow / 2);
	    out = (out * out) % mod;
	    if(pow % 2 == 1) out = (out * base) % mod;
	    return out;
	}
	static class edge{
	    int v, c;
	    edge(int vv, int cc){
	        v = vv;
	        c = cc;
	    }
	}
	static int p(String in){
	    return Integer.parseInt(in);
	}
}