#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
using namespace std;
char _buf[100000], *_p1 = _buf, *_p2 = _buf;
inline int gi() {
  int x = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = (x << 3) + (x << 1) + (ch ^ 48);
    ch = getchar();
  }
  return (f == 1) ? x : -x;
}
const int maxn = 2e5 + 5, inf = 1e9, mod = 1e9 + 7;
int n, k, a[maxn];
vector<pair<int, int>> e[maxn];
int siz[maxn], maxv[maxn], rt, dis[maxn];
long long val[maxn], ans;
vector<int> now;
struct segmentree {
  static const int maxn = 8e5 + 5;
  long long sum[maxn];
  inline void pushup(int u) { sum[u] = sum[u << 1] + sum[u << 1 | 1]; }
  inline void update(int u, int l, int r, int x, long long v) {
    if (l == r) return sum[u] += v, void();
    int mid = (l + r) >> 1;
    if (x <= mid)
      update(u << 1, l, mid, x, v);
    else
      update(u << 1 | 1, mid + 1, r, x, v);
    pushup(u);
  }
  inline long long query(int u, int l, int r, int x, int y) {
    if (x <= l && y >= r) return sum[u];
    int mid = (l + r) >> 1;
    long long ret = 0;
    if (x <= mid) ret = query(u << 1, l, mid, x, y);
    if (y > mid) ret += query(u << 1 | 1, mid + 1, r, x, y);
    return ret;
  }
} tree[2], T[2];
inline void init() {}
inline void input() {
  n = gi(), k = gi();
  for (int i = 1; i <= n; ++i) a[i] = gi();
  for (int i = 1; i <= n - 1; ++i) {
    int u = gi(), v = gi(), w = gi();
    e[u].push_back({v, w});
    e[v].push_back({u, w});
  }
}
bool vis[maxn];
int sum;
inline void getrt(int u, int fa) {
  now.push_back(u);
  siz[u] = 1;
  maxv[u] = 0;
  for (auto x : e[u]) {
    int v = x.first;
    if (v == fa || vis[v]) continue;
    getrt(v, u);
    siz[u] += siz[v];
    maxv[u] = max(maxv[u], siz[v]);
  }
  maxv[u] = max(maxv[u], sum - siz[u]);
  if (maxv[u] < maxv[rt]) rt = u;
}
inline void getdis(int u, int fa, int nowc) {
  now.push_back(u);
  for (auto x : e[u]) {
    int v = x.first, w = x.second;
    if (v == fa || vis[v]) continue;
    val[v] = val[u] + a[v], dis[v] = dis[u] + (nowc != w);
    getdis(v, u, w);
  }
}
inline void count(int u) {
  vector<pair<int, int>> temp;
  dis[u] = 0, val[u] = 0;
  ans = (ans + a[u]) % mod;
  for (auto x : e[u]) {
    now.clear();
    int v = x.first, w = x.second;
    if (vis[v]) continue;
    dis[v] = 0, val[v] = a[v];
    getdis(v, u, w);
    for (int x : now) temp.push_back({w, x});
    for (int x : now)
      if (dis[x] <= k) ans = (ans + val[x] + a[u]) % mod;
    for (int x : now) {
      if (dis[x] > k) continue;
      long long sum = tree[w].query(1, 0, n, 0, k - dis[x]) +
                      1ll * T[w].query(1, 0, n, 0, k - dis[x]) * val[x];
      if (dis[x] < k)
        sum += tree[w ^ 1].query(1, 0, n, 0, k - dis[x] - 1) +
               1ll * T[w ^ 1].query(1, 0, n, 0, k - dis[x] - 1) * val[x];
      ans = (ans + sum) % mod;
    }
    for (int x : now)
      if (dis[x] <= k)
        tree[w].update(1, 0, n, dis[x], val[x] + a[u]),
            T[w].update(1, 0, n, dis[x], 1);
  }
  for (auto x : temp) {
    int w = x.first, v = x.second;
    if (dis[v] > k) continue;
    tree[w].update(1, 0, n, dis[v], -val[v] - a[u]);
    T[w].update(1, 0, n, dis[v], -1);
  }
}
inline void Divide(int u) {
  vis[u] = 1;
  count(u);
  for (auto x : e[u]) {
    int v = x.first;
    if (vis[v]) continue;
    maxv[rt = 0] = inf;
    sum = siz[v];
    getrt(v, u);
    Divide(rt);
  }
}
inline void solve() {
  maxv[rt = 0] = inf;
  sum = n;
  getrt(1, 0);
  Divide(rt);
  printf("%lld\n", ans);
}
int main() {
  int T = 1;
  while (T--) {
    init();
    input();
    solve();
  }
  return 0;
}

### Prompt

Please formulate a cpp solution to 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>
#pragma GCC optimize("Ofast")
using namespace std;
char _buf[100000], *_p1 = _buf, *_p2 = _buf;
inline int gi() {
  int x = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = (x << 3) + (x << 1) + (ch ^ 48);
    ch = getchar();
  }
  return (f == 1) ? x : -x;
}
const int maxn = 2e5 + 5, inf = 1e9, mod = 1e9 + 7;
int n, k, a[maxn];
vector<pair<int, int>> e[maxn];
int siz[maxn], maxv[maxn], rt, dis[maxn];
long long val[maxn], ans;
vector<int> now;
struct segmentree {
  static const int maxn = 8e5 + 5;
  long long sum[maxn];
  inline void pushup(int u) { sum[u] = sum[u << 1] + sum[u << 1 | 1]; }
  inline void update(int u, int l, int r, int x, long long v) {
    if (l == r) return sum[u] += v, void();
    int mid = (l + r) >> 1;
    if (x <= mid)
      update(u << 1, l, mid, x, v);
    else
      update(u << 1 | 1, mid + 1, r, x, v);
    pushup(u);
  }
  inline long long query(int u, int l, int r, int x, int y) {
    if (x <= l && y >= r) return sum[u];
    int mid = (l + r) >> 1;
    long long ret = 0;
    if (x <= mid) ret = query(u << 1, l, mid, x, y);
    if (y > mid) ret += query(u << 1 | 1, mid + 1, r, x, y);
    return ret;
  }
} tree[2], T[2];
inline void init() {}
inline void input() {
  n = gi(), k = gi();
  for (int i = 1; i <= n; ++i) a[i] = gi();
  for (int i = 1; i <= n - 1; ++i) {
    int u = gi(), v = gi(), w = gi();
    e[u].push_back({v, w});
    e[v].push_back({u, w});
  }
}
bool vis[maxn];
int sum;
inline void getrt(int u, int fa) {
  now.push_back(u);
  siz[u] = 1;
  maxv[u] = 0;
  for (auto x : e[u]) {
    int v = x.first;
    if (v == fa || vis[v]) continue;
    getrt(v, u);
    siz[u] += siz[v];
    maxv[u] = max(maxv[u], siz[v]);
  }
  maxv[u] = max(maxv[u], sum - siz[u]);
  if (maxv[u] < maxv[rt]) rt = u;
}
inline void getdis(int u, int fa, int nowc) {
  now.push_back(u);
  for (auto x : e[u]) {
    int v = x.first, w = x.second;
    if (v == fa || vis[v]) continue;
    val[v] = val[u] + a[v], dis[v] = dis[u] + (nowc != w);
    getdis(v, u, w);
  }
}
inline void count(int u) {
  vector<pair<int, int>> temp;
  dis[u] = 0, val[u] = 0;
  ans = (ans + a[u]) % mod;
  for (auto x : e[u]) {
    now.clear();
    int v = x.first, w = x.second;
    if (vis[v]) continue;
    dis[v] = 0, val[v] = a[v];
    getdis(v, u, w);
    for (int x : now) temp.push_back({w, x});
    for (int x : now)
      if (dis[x] <= k) ans = (ans + val[x] + a[u]) % mod;
    for (int x : now) {
      if (dis[x] > k) continue;
      long long sum = tree[w].query(1, 0, n, 0, k - dis[x]) +
                      1ll * T[w].query(1, 0, n, 0, k - dis[x]) * val[x];
      if (dis[x] < k)
        sum += tree[w ^ 1].query(1, 0, n, 0, k - dis[x] - 1) +
               1ll * T[w ^ 1].query(1, 0, n, 0, k - dis[x] - 1) * val[x];
      ans = (ans + sum) % mod;
    }
    for (int x : now)
      if (dis[x] <= k)
        tree[w].update(1, 0, n, dis[x], val[x] + a[u]),
            T[w].update(1, 0, n, dis[x], 1);
  }
  for (auto x : temp) {
    int w = x.first, v = x.second;
    if (dis[v] > k) continue;
    tree[w].update(1, 0, n, dis[v], -val[v] - a[u]);
    T[w].update(1, 0, n, dis[v], -1);
  }
}
inline void Divide(int u) {
  vis[u] = 1;
  count(u);
  for (auto x : e[u]) {
    int v = x.first;
    if (vis[v]) continue;
    maxv[rt = 0] = inf;
    sum = siz[v];
    getrt(v, u);
    Divide(rt);
  }
}
inline void solve() {
  maxv[rt = 0] = inf;
  sum = n;
  getrt(1, 0);
  Divide(rt);
  printf("%lld\n", ans);
}
int main() {
  int T = 1;
  while (T--) {
    init();
    input();
    solve();
  }
  return 0;
}

```