description: There is a city park represented as a tree with n attractions as its vertices and n - 1 rails as its edges. The i-th attraction has happiness value a_i.
  
  Each rail has a color. It is either black if t_i = 0, or white if t_i = 1. Black trains only operate on a black rail track, and white trains only operate on a white rail track. If you are previously on a black train and want to ride a white train, or you are previously on a white train and want to ride a black train, you need to use 1 ticket.
  
  The path of a tour must be a simple path — it must not visit an attraction more than once. You do not need a ticket the first time you board a train. You only have k tickets, meaning you can only switch train types at most k times. In particular, you do not need a ticket to go through a path consisting of one rail color.
  
  Define f(u, v) as the sum of happiness values of the attractions in the tour (u, v), which is a simple path that starts at the u-th attraction and ends at the v-th attraction. Find the sum of f(u,v) for all valid tours (u, v) (1 ≤ u ≤ v ≤ n) that does not need more than k tickets, modulo 10^9 + 7.
  
  Input
  
  The first line contains two integers n and k (2 ≤ n ≤ 2 ⋅ 10^5, 0 ≤ k ≤ n-1) — the number of attractions in the city park and the number of tickets you have.
  
  The second line contains n integers a_1, a_2,…, a_n (0 ≤ a_i ≤ 10^9) — the happiness value of each attraction.
  
  The i-th of the next n - 1 lines contains three integers u_i, v_i, and t_i (1 ≤ u_i, v_i ≤ n, 0 ≤ t_i ≤ 1) — an edge between vertices u_i and v_i with color t_i. The given edges form a tree.
  
  Output
  
  Output an integer denoting the total happiness value for all valid tours (u, v) (1 ≤ u ≤ v ≤ n), modulo 10^9 + 7.
  
  Examples
  
  Input
  
  
  5 0
  1 3 2 6 4
  1 2 1
  1 4 0
  3 2 1
  2 5 0
  
  
  Output
  
  
  45
  
  
  Input
  
  
  3 1
  1 1 1
  1 2 1
  3 2 0
  
  
  Output
  
  
  10
solution: #include <bits/stdc++.h>
  using namespace std;
  const int modP = 1e9 + 7;
  const long long oo = 1000000000000000LL;
  const int maxN = 2e5 + 10;
  int n, k, res, sze[maxN], a[maxN], T[2][maxN], S[2][maxN], checkT[2][maxN],
      flag;
  vector<pair<int, int>> adj[maxN];
  bool elim[maxN];
  void build(int u, int p) {
    sze[u] = 1;
    for (auto [v, _] : adj[u])
      if (!elim[v] && v != p) build(v, u), sze[u] += sze[v];
  }
  void initBIT(int t, int x) {
    if (flag != checkT[t][x]) {
      checkT[t][x] = flag;
      T[t][x] = 0;
      S[t][x] = 0;
    }
  }
  void updateBIT(int t, int x, int v) {
    if (x == 0) {
      initBIT(t, 0);
      ++T[t][x];
      S[t][x] = (S[t][x] + v) % modP;
      return;
    }
    for (; x <= n; x += (x & -x)) {
      initBIT(t, x);
      ++T[t][x];
      S[t][x] = (S[t][x] + v) % modP;
    }
  }
  pair<int, int> getBIT(int t, int x) {
    if (x < 0) return {0, 0};
    initBIT(t, 0);
    int tmpT = T[t][0], tmpS = S[t][0];
    for (; x > 0; x -= (x & (-x))) {
      initBIT(t, x);
      tmpT = (tmpT + T[t][x]) % modP;
      tmpS = (tmpS + S[t][x]) % modP;
    }
    return {tmpT, tmpS};
  }
  void count(int u, int p, int oc, int pc, int cnt, int sum) {
    res = (res + sum) % modP;
    {
      auto [t, s] = getBIT(oc, k - cnt);
      res = (1ll * t * sum + res) % modP;
      res = (res + s) % modP;
    }
    {
      auto [t, s] = getBIT(1 - oc, k - cnt - 1);
      res = (1ll * t * sum + res) % modP;
      res = (res + s) % modP;
    }
    for (auto [v, w] : adj[u]) {
      if (!elim[v] && v != p) {
        int ncnt = cnt + (w != pc);
        if (ncnt > k) continue;
        count(v, u, oc, w, ncnt, (sum + a[v]) % modP);
      }
    }
  }
  void update(int u, int p, int oc, int pc, int cnt, int sum) {
    updateBIT(oc, cnt, sum);
    for (auto [v, w] : adj[u]) {
      if (!elim[v] && v != p) {
        int ncnt = cnt + (w != pc);
        if (ncnt > k) continue;
        update(v, u, oc, w, ncnt, (sum + a[v]) % modP);
      }
    }
  }
  int get_centroid(int u, int p, int num) {
    for (auto [v, _] : adj[u])
      if (!elim[v] && v != p && sze[v] > num / 2) return get_centroid(v, u, num);
    return u;
  }
  void centroid_decomposition(int u) {
    build(u, -1);
    ++flag;
    int root = get_centroid(u, -1, sze[u]);
    for (auto [v, w] : adj[root])
      if (!elim[v]) {
        count(v, root, w, w, 0, (a[root] + a[v]) % modP);
        update(v, root, w, w, 0, a[v]);
      }
    res = (res + a[root]) % modP;
    elim[root] = true;
    for (auto [v, _] : adj[root])
      if (!elim[v]) centroid_decomposition(v);
  }
  int main() {
    ios::sync_with_stdio(0);
    cin >> n >> k;
    for (int i = 1; i <= n; ++i) cin >> a[i];
    for (int i = 0; i < n - 1; ++i) {
      int u, v, w;
      cin >> u >> v >> w;
      adj[u].push_back({v, w});
      adj[v].push_back({u, w});
    }
    centroid_decomposition(1);
    cout << res << endl;
  }
  