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 Solution {

    private final long MODULO = (long) 1e9 + 7;
    private int N, K;
    private long count;
    private ArrayList<ArrayList<NodeInfo>> tree;
    private boolean[] visited;

    protected Solution(InputReader in) {
        N = in.nextInt();
        K = in.nextInt();
        tree = new ArrayList<ArrayList<NodeInfo>>(N);
        for (int j = 0; j < N; j++) {
            tree.add(new ArrayList<NodeInfo>());
        }
        for (int j = 0; j < N - 1; j++) {
            int a = in.nextInt(), b = in.nextInt(), color = in.nextInt();
            a--; b--;
            tree.get(a).add(new NodeInfo(b, color));
            tree.get(b).add(new NodeInfo(a, color));
        }
    }

    private long modPow(int a, int b) {
        long p = 1;
        for (int j = 0; j < b; j++) {
            p = (p * a) % MODULO;
        }
        return p;
    }

    private int dfs(int current) {
        visited[current] = true;
        int size = 1;
        for (NodeInfo next: tree.get(current)) {
            if (!visited[next.node] && next.color == 0) {
                size += dfs(next.node);
            }
        }
        return size;
    }

    public long solve() {
        count = 0;
        visited = new boolean[N];
        for (int j = 0; j < N; j++) {
            if (!visited[j]) {
                int cs = dfs(j);
                count = (count + modPow(cs, K)) % MODULO;
            }
        }
        return (modPow(N, K) + MODULO - count) % MODULO;
    }

    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);
        Solution solution = new Solution(in);
        out.println(solution.solve());
        out.close();
    }

}

class NodeInfo {
    int node, color;

    public NodeInfo(int node, int color) {
        this.node = node;
        this.color = color;
    }
}

class InputReader {

    private static final int BUFFER_SIZE = 1<<16;

    public BufferedReader reader;
    public StringTokenizer tokenizer;

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

    public 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());
    }

}
