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>
using namespace std;
void canhazfast() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
}
template <typename T>
T gcd(T a, T b) {
  return b ? gcd(b, a % b) : a;
}
template <typename T>
T extgcd(T a, T b, T &x, T &y) {
  T x0 = 1, y0 = 0, x1 = 0, y1 = 1;
  while (b) {
    T q = a / b;
    a %= b;
    swap(a, b);
    x0 -= q * x1;
    swap(x0, x1);
    y0 -= q * y1;
    swap(y0, y1);
  }
  x = x0;
  y = y0;
  return a;
}
int ctz(unsigned x) { return __builtin_ctz(x); }
int ctzll(unsigned long long x) { return __builtin_ctzll(x); }
int clz(unsigned x) { return __builtin_clz(x); }
int clzll(unsigned long long x) { return __builtin_clzll(x); }
int popcnt(unsigned x) { return __builtin_popcount(x); }
int popcntll(unsigned long long x) { return __builtin_popcountll(x); }
int bsr(unsigned x) { return 31 ^ clz(x); }
int bsrll(unsigned long long x) { return 63 ^ clzll(x); }
unsigned add(unsigned a, unsigned b) {
  return a + b < 1000000007 ? a + b : a + b - 1000000007;
}
unsigned sub(unsigned a, unsigned b) {
  return a < b ? a + 1000000007 - b : a - b;
}
unsigned mul(unsigned a, unsigned b) {
  return (unsigned long long)a * b % 1000000007;
}
unsigned sqr(unsigned a) { return mul(a, a); }
unsigned modpow(unsigned b, unsigned e) {
  unsigned r = 1;
  for (; e; e >>= 1) {
    if (e & 1) r = mul(r, b);
    b = mul(b, b);
  }
  return r;
}
unsigned modinv(unsigned n) { return modpow(n, 1000000007 - 2); }
unsigned moddiv(unsigned n, unsigned d) { return mul(n, modinv(d)); }
int sz[100016];
vector<pair<int, int> > adj[100016];
void dfs(int u, int p = 0) {
  sz[u] = 1;
  for (pair<int, int> &e : adj[u]) {
    int v = e.first, x = e.second;
    if (v == p || x != 0) continue;
    dfs(v, u);
    sz[u] += sz[v];
  }
}
int main() {
  canhazfast();
  int n, k;
  unsigned ans;
  vector<int> ccs;
  cin >> n >> k;
  for (int i = 1; i < n; ++i) {
    int u, v, x;
    cin >> u >> v >> x;
    adj[u].emplace_back(v, x);
    adj[v].emplace_back(u, x);
  }
  for (int i = 1; i <= n; ++i) {
    if (sz[i]) continue;
    dfs(i);
    ccs.push_back(sz[i]);
  }
  ans = modpow(n, k);
  for (int s : ccs) ans = sub(ans, modpow(s, k));
  cout << ans;
  return 0;
}
