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 double eps = 1e-9;
  const long long INFll = 4e18;
  const long long INFi = 1e9 + 63;
  const double pi = acos(-1);
  const int maxn = 6e5;
  const int maxd = 16;
  const long long mod = 1e9 + 7;
  const int sqrtN = 300;
  int caseNo = 1;
  void E() {}
  template <class A, class... B>
  void E(A $, B... _) {
    cerr << ' ' << $;
    E(_...);
  }
  const int mask = 1 << 5;
  int val[maxn];
  int del[maxn];
  int sz[maxn];
  vector<pair<int, int>> g[maxn];
  void dfs(int v, int p) {
    sz[v] = 1;
    for (auto& it : g[v]) {
      if (it.first == p || del[it.first]) continue;
      dfs(it.first, v);
      sz[v] += sz[it.first];
    }
  }
  int findCentroid(int v, int sz0, int p) {
    int mx = -1;
    for (auto& it : g[v]) {
      if (it.first == p || del[it.first]) continue;
      if (sz[it.first] > sz0 / 2 && (mx == -1 || sz[it.first] > sz[mx]))
        mx = it.first;
    }
    if (mx == -1)
      return v;
    else
      return findCentroid(mx, sz0, v);
  }
  void dfsCentr2(vector<long long>& res, vector<long long>& resPCnts, int v,
                 int prevC, int p, int d, long long acc) {
    if (((int)(res).size()) <= d) {
      res.resize(d + 1, 0);
    }
    if (((int)(resPCnts).size()) <= d) {
      resPCnts.resize(d + 1, 0);
    }
    acc += val[v];
    acc %= mod;
    res[d] += acc;
    resPCnts[d]++;
    resPCnts[d] %= mod;
    for (auto& it : g[v]) {
      if (it.first == p || del[it.first]) continue;
      dfsCentr2(res, resPCnts, it.first, it.second, v,
                d + ((prevC != it.second) ? 1 : 0), acc);
    }
  }
  int k;
  long long mul(int v, const vector<vector<long long>>& cntsA,
                const vector<vector<long long>>& cntsA2,
                const vector<vector<long long>>& cntsB,
                const vector<vector<long long>>& cntsB2) {
    vector<vector<long long>> cntsB2Sum = cntsB2;
    vector<vector<long long>> cntsBSum = cntsB;
    long long res = 0;
    for (int i = 0; i < 2; i++) {
      for (int j = 1; j < ((int)(cntsB2[i]).size()); j++) {
        cntsB2Sum[i][j] += cntsB2Sum[i][j - 1];
        cntsB2Sum[i][j] %= mod;
      }
      for (int j = 1; j < ((int)(cntsB[i]).size()); j++) {
        cntsBSum[i][j] += cntsBSum[i][j - 1];
        cntsBSum[i][j] %= mod;
      }
    }
    for (int i = 0; i < 2; i++) {
      for (int j = 0; j < 2; j++) {
        int extraLen = i == j ? 0 : 1;
        for (int it = 0; it <= min(((int)(cntsA[i]).size()) - 1, k); it++) {
          int remCnt = k - it - extraLen;
          if (remCnt < 0) break;
          if (remCnt >= ((int)(cntsB[j]).size()))
            remCnt = ((int)(cntsB[j]).size()) - 1;
          if (remCnt < 0) continue;
          assert(it < ((int)(cntsA[i]).size()) && it >= 0);
          assert(remCnt < ((int)(cntsB[j]).size()) && remCnt >= 0);
          res += (cntsA[i][it] * cntsB2Sum[j][remCnt]) % mod;
          res %= mod;
          res += (cntsBSum[j][remCnt] * cntsA2[i][it]) % mod;
          res %= mod;
          res -= (val[v] * (cntsA2[i][it] * cntsB2Sum[j][remCnt] % mod)) % mod;
          res %= mod;
          if (res < 0) res += mod;
        }
      }
    }
    return res;
  }
  long long res = 0;
  void dfsCentr(int v) {
    dfs(v, -1);
    int c = findCentroid(v, sz[v], -1);
    del[c] = true;
    vector<vector<long long>> acc(2);
    vector<vector<long long>> accPCnts(2);
    long long localRes = val[c];
    for (auto& it : g[c]) {
      if (del[it.first]) continue;
      vector<vector<long long>> tmp(2), tmpPCnts(2);
      dfsCentr2(tmp[it.second], tmpPCnts[it.second], it.first, it.second, c, 0,
                val[c]);
      for (int i = 0; i <= min(((int)(tmp[it.second]).size()) - 1, k); i++) {
        localRes += tmp[it.second][i];
        localRes %= mod;
      }
      localRes += mul(c, acc, accPCnts, tmp, tmpPCnts);
      localRes %= mod;
      for (int j = 0; j < 2; j++) {
        if (((int)(tmp[j]).size()) > ((int)(acc[j]).size())) tmp[j].swap(acc[j]);
        if (((int)(tmpPCnts[j]).size()) > ((int)(accPCnts[j]).size()))
          tmpPCnts[j].swap(accPCnts[j]);
        for (int i = 0; i < ((int)(tmp[j]).size()); i++) {
          acc[j][i] += tmp[j][i];
          acc[j][i] %= mod;
        }
        for (int i = 0; i < ((int)(tmpPCnts[j]).size()); i++) {
          accPCnts[j][i] += tmpPCnts[j][i];
          accPCnts[j][i] %= mod;
        }
      }
    }
    res += localRes;
    res %= mod;
    del[c] = true;
    for (auto& it : g[c]) {
      if (del[it.first]) continue;
      dfsCentr(it.first);
    }
  }
  int solveMy() {
    res = 0;
    dfsCentr(0);
    return res;
  }
  void solve() {
    int n;
    cin >> n >> k;
    for (int i = 0; i < n; i++) {
      cin >> val[i];
    }
    for (int i = 0; i < n - 1; i++) {
      int u, v, t;
      cin >> u >> v >> t;
      u--;
      v--;
      g[u].push_back({v, t});
      g[v].push_back({u, t});
    }
    cout << solveMy();
  }
  int main(int argc, char** argv) {
    cin.tie(0);
    cout.tie(0);
    ios_base::sync_with_stdio(false);
    cout << setprecision(15) << fixed;
    int t = 1;
    clock_t start = clock();
    for (int i = 0; i < t; i++) solve();
    return 0;
  }
  