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 org.omg.PortableInterceptor.INACTIVE;

import java.io.BufferedReader;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.*;

public class Main {
    static int []belong;
    static int []fac = new int[105];
    static int []inv = new int[105];
    static int find(int x){
        return x==belong[x]?x:(belong[x] = find(belong[x]));
    }
    static final int mod = 1000000007;

    static int mult(int a,int b){
        return (int)((long)a*b%mod);
    }
    static void unity(int a,int b){
        int pa = find(a);
        int pb = find(b);
        if(pa!=pb)belong[pa] = pb;
    }
    static void init(){
        fac[0] = 1;
        for(int i = 1 ; i <= 100 ; ++i){
            fac[i] = mult(fac[i-1],i);
        }
        inv[100] = kissMe(fac[100],mod-2);
        for(int i = 99 ; i >= 0 ; --i){
            inv[i] = mult(inv[i+1],i+1);
        }
    }
    static int kissMe(int a,int b){
        int odd = 1;
        while (b!=0){
            if((b&1)==1){
                odd=mult(odd,a);
            }
            a = mult(a,a);
            b>>=1;
        }
        return odd;
    }
    static int C(int a,int b){
        return mult(fac[a],mult(inv[a-b],inv[b]));
    }
    public static void main(String[] args) {
        int n,k;

        long ans = 0;
        init();
        String s;
        Scanner cin = new Scanner(System.in);
        n = cin.nextInt();
        k = cin.nextInt();
        belong = new int[n+1];
        for(int i = 0 ; i <= n ; ++i)belong[i] = i;
        Map<Integer,Integer> Res = new HashMap<Integer, Integer>();
        int u,v,c;
        for(int i = 1 ; i < n ;++i){
            u = cin.nextInt();
            v = cin.nextInt();
            c = cin.nextInt();
            if(c==0){
                unity(u,v);
            }
        }
        for(int i = 1 ; i <= n ; ++i){
            belong[i] = find(i);
            if(Res.containsKey(belong[i])){
                int sa = Res.get(belong[i])+1;
                Res.put(belong[i],sa);
            }else Res.put(belong[i],1);
        }
        Set<Integer> set = Res.keySet();
        Iterator<Integer> it= set.iterator();
        int total = n;
        while (it.hasNext()){
            int cs = it.next();
            cs = Res.get(cs);
            for(int i = 1 ; i < k ; ++i){
                ans+=mult(mult(kissMe(cs,i),kissMe(total-cs,k-i)),C(k,i));
            }
            total -= cs;
        }
        System.out.println(ans);
    }

}