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.IOException;
import java.io.InputStream;
import java.util.*;

public class edgytrees {
    public static void main(String[] args) {
        FastScanner in = new FastScanner(System.in);
        int n = in.nextInt();
        long k = in.nextInt();
        long mod = 1000000007;

        ArrayList<Edge>[] 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 c = in.nextInt();

            graph[u].add(new Edge(v,c));
            graph[v].add(new Edge(u,c));
        }

        long total = pow(n,k,mod);

        boolean[] vis = new boolean[n];
        for(int i = 0; i < n; i++) {
            if(vis[i])
                continue;
            Queue<Integer> q = new LinkedList<>();
            q.add(i);
            long size = 0;

            while(!q.isEmpty()) {
                int at = q.poll();
                if(vis[at])
                    continue;
                vis[at] = true;
                size++;
                for(Edge node : graph[at]) {
                    if(!vis[node.to] && node.color != 1) {
                        q.add(node.to);
                    }
                }
            }
            total = ((total-pow(size,k,mod) % mod)+mod)%mod;
        }
        System.out.println(total);

    }
    static long pow(long x, long y, long p) {
        long res = 1;
        x = x % p;

        if (x == 0)
            return 0;

        while (y > 0) {
            if((y & 1)==1)
                res = (res * x) % p;

            y = y >> 1;
            x = (x * x) % p;
        }
        return res;
    }

    static class Edge {
        int to, color;
        public Edge(int to, int color) {
            this.to = to;
            this.color = color;
        }
    }



    static class FastScanner {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public FastScanner(InputStream stream) {
            this.stream = stream;
        }

        int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        boolean isEndline(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

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

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

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

        String next() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        String nextLine() {
            int c = read();
            while (isEndline(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndline(c));
            return res.toString();
        }
    }
}
