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.util.*;
import java.io.*;

public class Main {
    public static void main(String[] args) throws IOException {
        FastScanner in = new FastScanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        new Main().run(in, out);
        out.close();
    }

    public static int mod = 1_000_000_007;

    class Edge {
        int v;
        int c;
        Edge(int v, int c) {
            this.v = v;
            this.c = c;
        }
    }
    List<Edge>[] adj;
    void run(FastScanner in, PrintWriter out) {
        N = in.nextInt();
        K = in.nextInt();

        adj = new List[N+1];
        for (int i = 0; i < adj.length; i++) adj[i] = new ArrayList<>();
        for (int i = 0; i < N-1; i++) {
            int u = in.nextInt();
            int v = in.nextInt();
            int c = in.nextInt();
            adj[u].add(new Edge(v, c == 0 ? RED : BLK));
            adj[v].add(new Edge(u, c == 0 ? RED : BLK));
        }

        dfs(1, -1, BLK);

        long tot = modpow(N, K);
        long ans = (((tot - cntbad)%mod)+mod)%mod;
        out.println(ans);
    }

    long cntbad = 0;
    int N, K;

    int dfs(int u, int p, int pc) {

        int sz = 1;
        for (Edge e : adj[u]) {
            if (e.v == p) continue;
            sz += dfs(e.v, u, e.c);
        }

        if (pc == BLK) {
            cntbad = (cntbad + modpow(sz, K))%mod;
            sz = 0;
        }

        return sz;
    }




    int RED = 0;
    int BLK = 1;

    long modpow(long x, int pow) {
        long ret = 1;
        while (pow > 0) {
            if ((pow&1) == 1) ret = (ret*x)%mod;
            x = (x*x)%mod;
            pow >>=1;
        }
        return ret;
    }

    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(InputStream in) {
            br = new BufferedReader(new InputStreamReader(in));
            st = null;
        }

        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());
        }
    }
}
