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.StringTokenizer;
import javafx.util.Pair;

public class Solve5 {

    public static void main(String[] args) throws IOException {
        PrintWriter pw = new PrintWriter(System.out);
        new Solve5().solve(pw);
        pw.flush();
        pw.close();
    }

    public void solve(PrintWriter pw) throws IOException {
        FastReader sc = new FastReader();
        final int MOD = (int) 1E+9 + 7;
        int n = sc.nextInt(), k = sc.nextInt();
        Pair<Pair<Integer, Integer>, Integer>[] edges = new Pair[n];
        for (int i = 1; i <= n - 1; i++) {
            edges[i] = new Pair(new Pair(sc.nextInt(), sc.nextInt()), sc.nextInt());
        }
        int[] parent = new int[n + 1];
        int[] size = new int[n + 1];
        for (int i = 1; i <= n; i++) {
            parent[i] = i;
            size[i] = 1;
        }
        for (int i = 1; i <= n - 1; i++) {
            if (edges[i].getValue() == 0) {
                Pair<Integer, Integer> temp = edges[i].getKey();
                merge(temp.getKey(), temp.getValue(), parent, size);
            }
        }
        long s = 0;
        for (int i = 1; i <= n; i++) {
            if (parent[i] == i) {
                s += pow(size[i], k, MOD);
                s %= MOD;
            }
        }
        long ans = pow(n, k, MOD) - s;
        pw.println(ans);
    }

    public long pow(long a, int p, int MOD) {
        int k = p;
        long ans = 1;
        while (k > 0) {
            if ((k & 1) == 1) {
                ans *= a;
                ans %= MOD;
            }
            a *= a;
            a %= MOD;
            k >>= 1;
        }
        return ans;
    }

    public int getParent(int x, int[] parent) {
        if (x == parent[x]) {
            return x;
        }
        return parent[x] = getParent(parent[x], parent);
    }

    public void merge(int x, int y, int[] parent, int[] size) {
        x = getParent(x, parent);
        y = getParent(y, parent);
        if (size[x] < size[y]) {
            size[y] += size[x];
            parent[x] = y;
        } else {
            size[x] += size[y];
            parent[y] = x;
        }
    }

    static class FastReader {

        StringTokenizer st;
        BufferedReader br;

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

        public boolean hasNext() throws IOException {
            String s = br.readLine();
            if (s == null || s.isEmpty()) {
                return false;
            }
            st = new StringTokenizer(s);
            return true;
        }

        public String next() throws IOException {
            if (st == null || !st.hasMoreTokens()) {
                String s = br.readLine();
                if (s.isEmpty()) {
                    return null;
                }
                st = new StringTokenizer(s);
            }
            return st.nextToken();
        }

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

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

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

        public String nextLine() throws IOException {
            return br.readLine();
        }
    }
}
