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.
//package com.example.programming;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.List;
import java.util.Map;
import java.util.Queue;
import java.util.Scanner;


public class CodeforcesProblems {

    static long mod = 1000000007L;

    static class Node {
        ArrayList<Integer> adj = new ArrayList<>();
        boolean is = false;
    }

    static long getPower(long n, long k) {
        if(k==0) return 1L;
        if(k==1) return n;
        long half = k/2;
        long f = getPower(n, half) % mod;
        long s = getPower(n, half) % mod;
        long res = (f * s) % mod;
        if(k%2 == 1) res = (res * n) % mod;
        return res;
    }

    static int connectedNodes(Node[] tree, int start) {
        ArrayList<Integer> q = new ArrayList<>();
        int count = 1;
        q.add(start);
        tree[start].is = true;
        int c = 0;
        for(;c < q.size();) {
            int pos = q.get(c++);
            Node cur = tree[pos];
            for(int i : cur.adj) {
                if(!tree[i].is) {
                    count++;
                    tree[i].is = true;
                    q.add(i);
                }
            }
        }
        return count;
    }

    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String[] s = br.readLine().split(" ");
        int n = Integer.parseInt(s[0]);
        long k = Long.parseLong(s[1]);
        Node[] tree = new Node[n+1];
        for(int i = 1; i<=n; i++) tree[i] = new Node();
        for(int i = 0; i<n-1; i++) {
            s = br.readLine().split(" ");
            if(s[2].charAt(0) == '1') continue;
            int x = Integer.parseInt(s[0]);
            int y = Integer.parseInt(s[1]);
            tree[x].adj.add(y);
            tree[y].adj.add(x);
        }
        long res = getPower(n, k);
        long minus = 0;
        int count = 0;
        for(int i = 1; i<=n; i++) {
            if(tree[i].adj.size()>0 && !tree[i].is) {
                int x = connectedNodes(tree, i);
                long pow = getPower(x, k);
                minus = (minus + pow) % mod;
                count += x;
            }
        }
        count = n-count;
        res = res >= count ? res - count : mod + res - count;
        res = res >= minus ? res - minus : mod + res - minus;
        System.out.println(res);
    }
}
