#include <bits/stdc++.h>
using namespace std;
const int maxn = 410000;
const int mod = 1e9 + 7;
const int mod2 = (mod + 1) >> 1;
inline void add(int &a, const int &b) {
  a += b;
  if (a >= mod) a -= mod;
}
inline void dec(int &a, const int &b) {
  a -= b;
  if (a < 0) a += mod;
}
int n, K;
int a[maxn];
vector<pair<int, int> > V[maxn];
int v[maxn];
int siz[maxn], Siz, root;
void dfs(const int x, const int fa) {
  siz[x] = 1;
  for (auto y : V[x])
    if (y.first != fa && !v[y.first]) {
      dfs(y.first, x);
      siz[x] += siz[y.first];
    }
}
void findroot(const int x, const int fa) {
  int mxs = 0;
  for (auto y : V[x])
    if (y.first != fa && !v[y.first]) {
      findroot(y.first, x);
      mxs = max(mxs, siz[y.first]);
    }
  if (mxs * 2 <= Siz && (Siz - siz[x]) * 2 <= Siz) root = x;
}
int f[2][maxn], g[2][maxn], uf;
int sf[2][maxn], sg[2][maxn];
int tuf, trc;
int ans;
void add(const int x, const int fa, const int now, const int sumk,
         const int suma) {
  add(f[trc][sumk], suma);
  add(g[trc][sumk], 1);
  for (auto temp : V[x]) {
    int y = temp.first;
    if (y != fa && !v[y])
      add(y, x, temp.second, sumk + (now != temp.second), (suma + a[y]) % mod);
  }
  tuf = max(tuf, sumk);
}
void cal(const int x, const int fa, const int now, const int sumk,
         const int suma) {
  if (sumk > K) return;
  if (sumk <= K) add(ans, (long long)suma * 2 % mod);
  for (int j = 0; j < 2; j++)
    if (sumk + (j != trc) <= K) {
      int ui = min(uf, K - sumk + (j == trc));
      int tf = sf[j][ui], tg = sg[j][ui];
      dec(tf, f[j][min(ui, tuf)]);
      dec(tg, g[j][min(ui, tuf)]);
      add(ans, (long long)tg * suma % mod);
      add(ans, tf);
    }
  for (auto temp : V[x]) {
    int y = temp.first;
    if (y != fa && !v[y])
      cal(y, x, temp.second, sumk + (now != temp.second), (suma + a[y]) % mod);
  }
}
void Divide(int x) {
  dfs(x, 0);
  Siz = siz[x];
  findroot(x, 0);
  x = root;
  uf = Siz;
  for (auto temp : V[x]) {
    int y = temp.first;
    if (!v[y]) {
      trc = temp.second;
      add(y, x, temp.second, 1, a[y]);
    }
  }
  for (int j = 0; j < 2; j++) {
    sf[j][0] = f[j][0];
    sg[j][0] = g[j][0];
    f[j][0] = 0, g[j][0] = 0;
    for (int i = 1; i <= uf; i++) {
      sf[j][i] = (sf[j][i - 1] + f[j][i]) % mod;
      f[j][i] = 0;
      sg[j][i] = (sg[j][i - 1] + g[j][i]) % mod;
      g[j][i] = 0;
    }
  }
  for (auto temp : V[x]) {
    int y = temp.first;
    if (!v[y]) {
      tuf = 0;
      trc = temp.second;
      add(y, x, temp.second, 1, a[y]);
      for (int j = 0; j < 2; j++)
        for (int i = 1; i <= tuf; i++) {
          f[j][i] = (f[j][i - 1] + f[j][i]) % mod;
          g[j][i] = (g[j][i - 1] + g[j][i]) % mod;
        }
      cal(y, x, temp.second, 1, (a[x] + a[y]) % mod);
      for (int j = 0; j < 2; j++)
        for (int i = 0; i <= tuf; i++) {
          f[j][i] = g[j][i] = 0;
        }
    }
  }
  v[x] = 1;
  for (auto temp : V[x]) {
    int y = temp.first;
    if (!v[y]) Divide(y);
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin >> n >> K;
  K++;
  for (int i = 1; i <= n; i++) cin >> a[i];
  for (int i = 1; i < n; i++) {
    int x, y, ti;
    cin >> x >> y >> ti;
    V[x].push_back(make_pair(y, ti));
    V[y].push_back(make_pair(x, ti));
  }
  Divide(1);
  ans = (long long)ans * mod2 % mod;
  for (int i = 1; i <= n; i++) add(ans, a[i]);
  cout << ans << endl;
  return 0;
}

### Prompt

Develop a solution in CPP to the problem described below:

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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int maxn = 410000;
const int mod = 1e9 + 7;
const int mod2 = (mod + 1) >> 1;
inline void add(int &a, const int &b) {
  a += b;
  if (a >= mod) a -= mod;
}
inline void dec(int &a, const int &b) {
  a -= b;
  if (a < 0) a += mod;
}
int n, K;
int a[maxn];
vector<pair<int, int> > V[maxn];
int v[maxn];
int siz[maxn], Siz, root;
void dfs(const int x, const int fa) {
  siz[x] = 1;
  for (auto y : V[x])
    if (y.first != fa && !v[y.first]) {
      dfs(y.first, x);
      siz[x] += siz[y.first];
    }
}
void findroot(const int x, const int fa) {
  int mxs = 0;
  for (auto y : V[x])
    if (y.first != fa && !v[y.first]) {
      findroot(y.first, x);
      mxs = max(mxs, siz[y.first]);
    }
  if (mxs * 2 <= Siz && (Siz - siz[x]) * 2 <= Siz) root = x;
}
int f[2][maxn], g[2][maxn], uf;
int sf[2][maxn], sg[2][maxn];
int tuf, trc;
int ans;
void add(const int x, const int fa, const int now, const int sumk,
         const int suma) {
  add(f[trc][sumk], suma);
  add(g[trc][sumk], 1);
  for (auto temp : V[x]) {
    int y = temp.first;
    if (y != fa && !v[y])
      add(y, x, temp.second, sumk + (now != temp.second), (suma + a[y]) % mod);
  }
  tuf = max(tuf, sumk);
}
void cal(const int x, const int fa, const int now, const int sumk,
         const int suma) {
  if (sumk > K) return;
  if (sumk <= K) add(ans, (long long)suma * 2 % mod);
  for (int j = 0; j < 2; j++)
    if (sumk + (j != trc) <= K) {
      int ui = min(uf, K - sumk + (j == trc));
      int tf = sf[j][ui], tg = sg[j][ui];
      dec(tf, f[j][min(ui, tuf)]);
      dec(tg, g[j][min(ui, tuf)]);
      add(ans, (long long)tg * suma % mod);
      add(ans, tf);
    }
  for (auto temp : V[x]) {
    int y = temp.first;
    if (y != fa && !v[y])
      cal(y, x, temp.second, sumk + (now != temp.second), (suma + a[y]) % mod);
  }
}
void Divide(int x) {
  dfs(x, 0);
  Siz = siz[x];
  findroot(x, 0);
  x = root;
  uf = Siz;
  for (auto temp : V[x]) {
    int y = temp.first;
    if (!v[y]) {
      trc = temp.second;
      add(y, x, temp.second, 1, a[y]);
    }
  }
  for (int j = 0; j < 2; j++) {
    sf[j][0] = f[j][0];
    sg[j][0] = g[j][0];
    f[j][0] = 0, g[j][0] = 0;
    for (int i = 1; i <= uf; i++) {
      sf[j][i] = (sf[j][i - 1] + f[j][i]) % mod;
      f[j][i] = 0;
      sg[j][i] = (sg[j][i - 1] + g[j][i]) % mod;
      g[j][i] = 0;
    }
  }
  for (auto temp : V[x]) {
    int y = temp.first;
    if (!v[y]) {
      tuf = 0;
      trc = temp.second;
      add(y, x, temp.second, 1, a[y]);
      for (int j = 0; j < 2; j++)
        for (int i = 1; i <= tuf; i++) {
          f[j][i] = (f[j][i - 1] + f[j][i]) % mod;
          g[j][i] = (g[j][i - 1] + g[j][i]) % mod;
        }
      cal(y, x, temp.second, 1, (a[x] + a[y]) % mod);
      for (int j = 0; j < 2; j++)
        for (int i = 0; i <= tuf; i++) {
          f[j][i] = g[j][i] = 0;
        }
    }
  }
  v[x] = 1;
  for (auto temp : V[x]) {
    int y = temp.first;
    if (!v[y]) Divide(y);
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin >> n >> K;
  K++;
  for (int i = 1; i <= n; i++) cin >> a[i];
  for (int i = 1; i < n; i++) {
    int x, y, ti;
    cin >> x >> y >> ti;
    V[x].push_back(make_pair(y, ti));
    V[y].push_back(make_pair(x, ti));
  }
  Divide(1);
  ans = (long long)ans * mod2 % mod;
  for (int i = 1; i <= n; i++) add(ans, a[i]);
  cout << ans << endl;
  return 0;
}

```