#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;
}

### Prompt

Create a solution in CPP for the following problem:

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 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;
}

```