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.StringTokenizer;

public class C {
    String filename = "";

    final int INF = 1_000_000_000;
    final int MOD = 1_000_000_000 + 7;
    class DSU{
        int[] parents, sizes;
        boolean[] used;
        DSU(int n){
            parents = new int[n];
            sizes = new int[n];
            used = new boolean[n];
            for(int i = 0;i<n;i++){
                parents[i] = i;
                sizes[i] = 1;
            }
        }

        void unite(int a, int b){
            a = find(a);
            b = find(b);

            if(sizes[a] < sizes[b]){
                int tmp = a;
                a = b;
                b = tmp;
            }

            sizes[a] += sizes[b];
            parents[b] = a;
        }

        int find(int x){
            if(x == parents[x]) return x;
            return parents[x] = find(parents[x]);
        }

        int getSize(int x){
            x = find(x);
            if(used[x]) return 0;
            used[x] = true;
            return sizes[x];
        }
    }
    int getNum(int x, int k){
        int res = 1;
        for(int  i = 0;i<k;i++){
            res = res * x % MOD;
        }
        return res;
    }
    void solve() {
        int n = readInt();
        int k = readInt();

        DSU dsu = new DSU(n);
        for(int i = 0;i<n - 1;i++){
            int a = readInt() - 1;
            int b = readInt() - 1;
            int c = readInt();
            if(c == 0) dsu.unite(a, b);
        }

        int ans = getNum(n, k);
        for(int i  =0;i<n;i++){
            ans = (ans - getNum(dsu.getSize(i), k) + MOD) % MOD;
        }
        out.print(ans);
    }

    public static void main(String[] args) throws FileNotFoundException {
        new C().run();
    }
    void run() throws FileNotFoundException {
        init();
        solve();
        out.close();
    }
    BufferedReader in;
    PrintWriter out;

    StringTokenizer tok = new StringTokenizer("");

    void init() throws FileNotFoundException {
        if(!filename.equals("")) {
            in = new BufferedReader(new FileReader(new File(filename + ".in")));
            out = new PrintWriter(new File(filename + ".out"));
            return;
        }

        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
    }

    String readLine(){
        try{
            return in.readLine();
        }catch (Exception e){
            throw new RuntimeException(e);
        }
    }

    String readString(){
        while(!tok.hasMoreTokens()){
            String nextLine = readLine();
            if(nextLine == null) return null;
            tok = new StringTokenizer(nextLine);
        }
        return tok.nextToken();
    }

    int readInt(){
        return Integer.parseInt(readString());
    }

    long readLong(){
        return Long.parseLong(readString());
    }
}