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 {
    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(Reader in) {
            br = new BufferedReader(in);
        }

        public FastScanner() {
            this(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;
        }

        int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int idx = 0; idx < n; idx++) {
                a[idx] = nextInt();
            }
            return a;
        }
    }

    static int dfs(HashMap<Integer, ArrayList<Integer>> graph, int pos, Set<Integer> vis) {
        if (vis.contains(pos) || !graph.containsKey(pos)) {
            return 0;
        }
        int ans = 1;
        vis.add(pos);
        for (int x: graph.get(pos)) {
            ans += dfs(graph, x, vis);
        }
        return ans;
    }

    public static void main(String[] args) {
        /**
         * 3 5
            1 2 0
            2 3 0

            7 3
            1 2 0
            2 4 0
            2 6 0
            3 7 0
            3 6 1
            5 6 1
         */
        FastScanner sc = new FastScanner();

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

        HashMap<Integer, ArrayList<Integer>> graph = new HashMap<>();

        for (int i = 0; i < n - 1; i++) {
            int[] arr = sc.nextIntArray(3);
            int l = arr[0];
            int r = arr[1];
            int color = arr[2];
            if (color == 1) {
                continue;
            }
            if (!graph.containsKey(l)) {
                graph.put(l, new ArrayList<Integer>());
            }
            if (!graph.containsKey(r)) {
                graph.put(r, new ArrayList<Integer>());
            }
            graph.get(l).add(r);
            graph.get(r).add(l);
        }
        
        Set<Integer> vis = new HashSet<>();
        long ans = n;
        int mod = 1000000007;
        for (int i = 0; i < k - 1; i++) {
            ans *= n;
            ans %= mod;
        }
        ans -= n;

        for (int i = 1; i <= n; i++) {
            if (vis.contains(i)) {
                continue;
            }
            int g_size = dfs(graph, i, vis);
            long cnt_ans = g_size;
            for (int j = 0; j < k - 1; j++) {
                cnt_ans *= g_size;
                cnt_ans %= mod;
            }
            ans -= (cnt_ans - g_size);
        }

        System.out.println((ans + 2 * mod) % mod);
    }
}