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.*;
import java.util.*;

public class Main {

    static int mod = 1000000007;

    static int find_conn(ArrayList<Integer>[] tree, boolean[] vis, int ver){
        vis[ver] = true;
        int ans = 1;
        for(int x: tree[ver]){
            if(!vis[x]) ans += find_conn(tree, vis, x);
        }
        return ans;
    }

    static long exp(int a, int b){
        if(b == 0 || a == 1) return 1;
        if(b%2 == 1) return (a*(exp(a, b-1)))%mod;
        else{
            long x = exp(a, b/2);
            return (x*x)%mod;
        }
    }

    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String[] str = br.readLine().split(" ");
        int n = Integer.parseInt(str[0]), k = Integer.parseInt(str[1]);
        ArrayList<Integer>[] tree = new ArrayList[n];
        for(int i = 0; i<n; i++){
            tree[i] = new ArrayList<>();
        }
        for(int i = 0; i<n-1; i++){
            String[] st = br.readLine().split(" ");
            int u = Integer.parseInt(st[0])-1, v = Integer.parseInt(st[1])-1, c = Integer.parseInt(st[2]);
            if(c == 0){
                tree[v].add(u);
                tree[u].add(v);
            }
        }
        boolean[] vis = new boolean[n];
        ArrayList<Integer> lst =new ArrayList<>();
        for(int i = 0; i<n; i++) {
            if(!vis[i]) lst.add(find_conn(tree, vis, i));
        }
        long exp1 = exp(n, k)%mod;
        long exp2 = 0;
        for(int x: lst){
            exp2 = (exp2%mod + exp(x, k)%mod)%mod;
        }
        System.out.println((exp1-exp2+mod)%mod);
    }
}
