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.*;

public class C_EdgyTree {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader inp = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Solver solver = new Solver();
        solver.solve(inp, out);
        out.close();
    }

    private static class Solver {
        private void solve(InputReader inp, PrintWriter out) {
            int n = inp.nextInt(), k = inp.nextInt();
            DSU dsu = new DSU(n);
            for (int i = 0; i < n - 1; i++) {
                int u = inp.nextInt() - 1, v = inp.nextInt() - 1, x = inp.nextInt();
                if (x == 1) continue;
                if (!dsu.sameSet(u, v)) dsu.union(u, v);
            }
            ArrayList<Integer>[] sets = dsu.getSets();
            long res = 0;
            long MOD = 1000000007;
            long[] nPower = new long[k+1];
            nPower[0] = 1;
            for (int i = 1; i < k + 1; i++) nPower[i] = (nPower[i-1] * n) % MOD;
            for (ArrayList<Integer> set: sets) {
                long in = set.size();
                for (int i = 2; i <= k; i++) {
                    long temp = (in * (n - set.size())) % MOD;
                    temp = (temp * nPower[k - i]) % MOD;
                    res = (res + temp) % MOD;
                    in = (in * set.size()) % MOD;
                }
            }
            out.print(res);
        }

        public class DSU {
            private int[] parents, rank;

            public DSU(int n) {
                parents = new int[n];
                rank = new int[n];
                for (int i = 0; i < n; i++) parents[i] = -1;
            }

            public int findParent(int node) {
                if (parents[node] == -1) return node; //recursively search
                int parent = findParent(parents[node]);
                parents[node] = parent; //don't search another time for parent
                return parent;
            }

            public void union(int x, int y) {
                int xParent = findParent(x), yParent = findParent(y);
                if (rank[x] < rank[y]) parents[xParent] = yParent;
                else if (rank[x] > rank[y]) parents[yParent] = xParent;
                else {
                    parents[yParent] = xParent;
                    rank[xParent]++;
                }
            }

            public ArrayList<Integer>[] getSets() {
                HashMap<Integer, ArrayList<Integer>> sets = new HashMap<>();
                for (int i = 0; i < parents.length; i++) {
                    int parent = findParent(i);
                    if (!sets.containsKey(parent)) sets.put(parent, new ArrayList<>());
                    sets.get(parent).add(i);
                }
                int i = 0;
                ArrayList<Integer>[] res = new ArrayList[sets.size()];
                for (ArrayList<Integer> set: sets.values()) {
                    res[i] = set;
                    i++;
                }
                return res;
            }

            public boolean sameSet(int x, int y) {
                return findParent(x) == findParent(y);
            }
        }

    }

    static class InputReader {
        BufferedReader reader;
        StringTokenizer tokenizer;

        InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong() {
            return Long.parseLong(next());
        }
    }
}
