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.
#include <bits/stdc++.h>
template <class C>
inline void log_c(const C& c) {}
template <class C>
inline int sz(const C& c) {
  return static_cast<int>(c.size());
}
using namespace std;
using num = int64_t;
const std::string eol = "\n";
using pii = pair<int, int>;
num sum = 0;
vector<vector<int>> adj;
vector<bool> visited;
const num mod = 1000000000 + 7;
inline num pow_by_mod(num n, num exp) {
  num ax = 1;
  for (; exp; --exp) {
    ax = (ax * n) % mod;
  }
  return ax;
}
inline int tree_size(int u, int p) {
  int ans = 1;
  visited.at(u) = true;
  for (int v : adj.at(u)) {
    if (v == p) continue;
    ans += tree_size(v, u);
  }
  return ans;
}
int main() {
  std::ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  int n, m;
  cin >> n >> m;
  adj.resize(n);
  visited.resize(n);
  for (int k = 0; k < (n - 1); ++k) {
    int u, v, x;
    cin >> u >> v >> x;
    if (x == 0) {
      --u;
      --v;
      adj.at(u).push_back(v);
      adj.at(v).push_back(u);
    }
  }
  num bad_path_count = 0;
  for (int u = 0; u < (n); ++u) {
    if (visited.at(u)) continue;
    num sz = tree_size(u, u);
    bad_path_count = (bad_path_count + pow_by_mod(sz, m)) % mod;
  }
  const num path_count = pow_by_mod(n, m);
  const num good_path_count = (path_count - bad_path_count + mod) % mod;
  cout << good_path_count << endl;
  return 0;
}
