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 Main {
    static ArrayList<Integer> gr[];
    static boolean used[];
    static int cnt = 0;
    static public void dfs(int v) {
        if (used[v]) return;
        used[v] = true;
        cnt++;
        for(int i : gr[v]) {
            dfs(i);
        }
    }
    public static void main(String[] args) throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw = new PrintWriter(System.out);
        int n = nextInt();
        int k = nextInt();
        gr = new ArrayList[n];
        used = new boolean [n];
        for(int i = 0;i < n;i++) gr[i] = new ArrayList<>();
        for(int i = 0;i < n - 1;i++) {
            int v = nextInt() - 1;
            int u = nextInt() - 1;
            int c = nextInt();
            if (c == 1) continue;
            gr[v].add(u);
            gr[u].add(v);
        }
        long ans = n;
        int st = 1;
        int mod = (int) 1e9 + 7;
        while(st != k) {
            ans = (ans * n) % mod;
            st++;
        }
        for(int i = 0;i < n;i++) {
            if (!used[i]) {
                cnt = 0;
                dfs(i);
                st = 1;
                long u = cnt;
                while(st != k) {
                    u = (u * cnt) % mod;
                    st++;
                }
                ans -= u;
            }
        }
        pw.println((ans % mod + mod) % mod);
        pw.close();
    }

    static BufferedReader br;
    static StringTokenizer st = new StringTokenizer("");

    public static int nextInt() throws IOException {
        if (!st.hasMoreTokens()) {
            st = new StringTokenizer(br.readLine());
        }
        return Integer.parseInt(st.nextToken());
    }

    public static long nextLong() throws IOException {
        if (!st.hasMoreTokens()) {
            st = new StringTokenizer((br.readLine()));
        }
        return Long.parseLong(st.nextToken());
    }

    public static double nextDouble() throws IOException {
        if (!st.hasMoreTokens()) {
            st = new StringTokenizer(br.readLine());
        }
        return Double.parseDouble(st.nextToken());
    }

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