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.*;
import java.math.*;

public final class Main {
    BufferedReader br;
    StringTokenizer stk;
    
    public static void main(String[] args) throws Exception {
        new Main().run();
    }
    
    {
        stk = null;
        br = new BufferedReader(new InputStreamReader(System.in));
    }
    
    boolean tests = false;
    
    long mod = 1000_000_000 + 7;
    StringBuilder res = new StringBuilder(1000005);
    
    void run() throws Exception {
        int t = tests ? ni() : 1;
        for(int i = 1; i <= t; i++) {
            go(i);
        }
        System.out.print(res.length() == 0 ? "" : res);
    }
    
    void go(int T) throws Exception {
        int n = ni(), k = ni();
        Node[] g = new Node[n + 1];
        for(int i = 1; i <= n; i++) {
            g[i] = new Node();
        }
        for(int i = 1; i < n; i++) {
            int u = ni(), v = ni(), x = ni();
            if(x == 0) {
                g[u].adj.add(v);
                g[v].adj.add(u);
            }
        }
        
        boolean[] visited = new boolean[n + 1];
        
        long ans = 0, total = modPow(n, k);
        for(int i = 1; i <= n; i++) {
            if(!visited[i]) {
                int N = recur(i, visited, g);
                ans += modPow(N, k);
                ans %= mod;
            }
        }
        
        ans = (total - ans + mod) % mod;
        
        res.append(ans).append("\n");
    }
    
    int recur(int node, boolean[] v, Node[] g) {
        if(v[node]) return 0;
        v[node] = true; // mark visited
        int value = 1;
        for(int adj : g[node].adj) {
            value += recur(adj, v, g);
        }
        return value;
    }
    
    long modPow(long x, long y) {
        if(y == 0) return 1;
        if(y == 1) return x;
        long val = modPow(x, y / 2);
        val = ((((val * val) % mod) * modPow(x, y % 2)) % mod);
        return val;
    }
    
    class Node {
        HashSet<Integer> adj;
        public Node() {
            adj = new HashSet<>();
        }
    }
    
    //Reader & Writer
    String nt() throws Exception {
        if (stk == null || !stk.hasMoreTokens())
            stk = new StringTokenizer(br.readLine(), " ");
        return stk.nextToken();
    }

    char[] nc() throws Exception {
        return nt().toCharArray();
    }

    int ni() throws Exception {
        return Integer.parseInt(nt());
    }

    long nl() throws Exception {
        return Long.parseLong(nt());
    }
    
    double nd() throws Exception {
        return Double.parseDouble(nt());
    }
    
    //Some Misc methods
    int get(int l, int r, int[] a) {
        return l == 0 ? a[r] : a[r] - a[l - 1];
    }
    
    void shuffle(int[] a) {
        Random r = new Random();
        for(int i = 0; i < a.length; i++) {
            int idx = r.nextInt(a.length);
            int temp = a[i];
            a[i] = a[idx];
            a[idx] = temp;
        }
    }
    
    void reverse(long[] a) {
        for(int i = 0, j = a.length - 1; i < j; i++, j--) {
            long temp = a[i];
            a[i] = a[j];
            a[j] = temp;
        }
    }
    
    void print(int[] a) {
        System.out.println(Arrays.toString(a));
    }
    
    void print(long[] a) {
        System.out.println(Arrays.toString(a));
    }
}