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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class pr1139C {
    static final long MOD = (long)1e9 + 7;
    static ArrayList<Integer> graph[];
    static boolean[] vis;
    static int cnt;
    public static void main(String[] args) {
        FastScanner in = new FastScanner();
        PrintWriter out = new PrintWriter(System.out);

        int n = in.nextInt();
        int k = in.nextInt();

        graph = new ArrayList[n];
        for (int i = 0; i < n; i++) {
            graph[i] = new ArrayList<>();
        }

        for (int i = 0; i < n - 1; i++) {
            int u = in.nextInt() - 1;
            int v = in.nextInt() - 1;
            int x = in.nextInt();

            if(x == 0) {
                graph[u].add(v);
                graph[v].add(u);
            }
        }

        out.println(solve(n, k));
        out.flush();
        out.close();
    }

    private static long solve(int n, int k) {
        long ans = fast_exp(n, k);

        vis = new boolean[n];
        long r = 0;
        for (int i = 0; i < n; i++) {
            if(!vis[i]) {
                cnt = 0;
                dfs(i);
                r += fast_exp(cnt, k);
            }
        }

        r %= MOD;
        return (ans - r + MOD) % MOD;
    }

    private static void dfs(int i) {
        vis[i] = true;
        cnt++;

        for(int j: graph[i]) {
            if(!vis[j])
                dfs(j);
        }
    }

    private static long fast_exp(int n, int k) {
        if(k == 1) {
            return (long) n;
        }
        long a = fast_exp(n, k/2);

        if(k % 2 == 0) {
            return a * a % MOD;
        }
//        return (a * a * (n % MOD)) % MOD;
        return a * a % MOD * n % MOD;
    }

    static class FastScanner
    {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner()
        {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt()
        {
            return Integer.parseInt(next());
        }

        long nextLong()
        {
            return Long.parseLong(next());
        }

        double nextDouble()
        {
            return Double.parseDouble(next());
        }

        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
}

