#include <bits/stdc++.h>
using namespace std;
long long tree[2][410000];
long long ans = 0;
vector<long long> del;
void update(long long &x, long long y) { (x += y) %= 1000000007; }
long long lowbit(long long x) { return x & (-x); }
void insert(long long typ, long long x) {
  x++;
  if (x <= 0) return;
  while (x < 410000) {
    del.push_back(x);
    tree[typ][x]++;
    x += lowbit(x);
  }
}
long long get(long long typ, long long x) {
  x++;
  if (x <= 0) return 0;
  long long ret = 0;
  while (x) {
    update(ret, tree[typ][x]);
    x -= lowbit(x);
  }
  return ret;
}
struct EDGE {
  long long adj, next, w, valid;
} edge[2 * 410000];
long long gh[410000], n, k, w[410000], top, maxdist, sizz[410000], son[410000];
void addedge(long long x, long long y, long long w) {
  edge[++top].adj = y;
  edge[top].valid = 1;
  edge[top].w = w;
  edge[top].next = gh[x];
  gh[x] = top;
}
void get_size(long long x, long long root = 0) {
  sizz[x] = 1;
  son[x] = 0;
  long long dd = 0;
  for (long long p = gh[x]; p; p = edge[p].next)
    if (edge[p].adj != root && edge[p].valid) {
      get_size(edge[p].adj, x);
      sizz[x] += sizz[edge[p].adj];
      if (sizz[edge[p].adj] > dd) {
        dd = sizz[edge[p].adj];
        son[x] = edge[p].adj;
      }
    }
}
long long getroot(long long x) {
  get_size(x);
  long long sz = sizz[x];
  while (sizz[son[x]] > sz / 2) x = son[x];
  return x;
}
vector<pair<long long, long long> > q[410000][2];
void dfs(long long x, long long pre, long long prec, long long sum,
         long long cnt, long long typ, long long root) {
  if (cnt > k) return;
  update(sum, w[x]);
  q[root][typ].push_back(make_pair(sum, cnt));
  for (long long p = gh[x]; p; p = edge[p].next) {
    if (edge[p].valid == 0) continue;
    if (edge[p].adj == pre) continue;
    dfs(edge[p].adj, x, edge[p].w, sum, cnt + (edge[p].w != prec), typ, root);
  }
}
void dc(long long x) {
  x = getroot(x);
  static long long list[410000], ltop;
  ltop = 0;
  for (long long p = gh[x]; p; p = edge[p].next)
    if (edge[p].valid) list[++ltop] = edge[p].adj;
  for (long long p = gh[x]; p; p = edge[p].next) {
    if (edge[p].valid == 0) continue;
    q[edge[p].adj][0].clear();
    q[edge[p].adj][1].clear();
    dfs(edge[p].adj, x, edge[p].w, 0, 0, edge[p].w, edge[p].adj);
    for (auto t : q[edge[p].adj][0]) update(ans, t.first + w[x]);
    for (auto t : q[edge[p].adj][1]) update(ans, t.first + w[x]);
  }
  update(ans, w[x]);
  for (long long t = 0; t <= 1; t++) {
    if (t == 1) reverse(list + 1, list + ltop + 1);
    del.clear();
    for (long long i = 1; i <= ltop; i++) {
      long long delta = 0;
      if (t == 0) delta = w[x];
      for (auto p : q[list[i]][0])
        update(ans, (p.first + delta) *
                        (get(0, k - p.second) + get(1, k - p.second - 1)) %
                        1000000007);
      for (auto p : q[list[i]][1])
        update(ans, (p.first + delta) *
                        (get(1, k - p.second) + get(0, k - p.second - 1)) %
                        1000000007);
      for (auto p : q[list[i]][0]) insert(0, p.second);
      for (auto p : q[list[i]][1]) insert(1, p.second);
    }
    for (auto p : del) tree[0][p] = tree[1][p] = 0;
  }
  for (long long p = gh[x]; p; p = edge[p].next)
    if (edge[p].valid) {
      edge[p].valid = 0;
      edge[p ^ 1].valid = 0;
      dc(edge[p].adj);
    }
}
signed main() {
  cin >> n >> k;
  for (long long i = 1; i <= n; i++) scanf("%lld", &w[i]);
  top = 1;
  for (long long i = 1; i < n; i++) {
    long long x, y, w;
    scanf("%lld%lld%lld", &x, &y, &w);
    addedge(x, y, w);
    addedge(y, x, w);
  }
  dc(1);
  cout << ans << endl;
  return 0;
}

### Prompt

In cpp, your task is to solve 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;
long long tree[2][410000];
long long ans = 0;
vector<long long> del;
void update(long long &x, long long y) { (x += y) %= 1000000007; }
long long lowbit(long long x) { return x & (-x); }
void insert(long long typ, long long x) {
  x++;
  if (x <= 0) return;
  while (x < 410000) {
    del.push_back(x);
    tree[typ][x]++;
    x += lowbit(x);
  }
}
long long get(long long typ, long long x) {
  x++;
  if (x <= 0) return 0;
  long long ret = 0;
  while (x) {
    update(ret, tree[typ][x]);
    x -= lowbit(x);
  }
  return ret;
}
struct EDGE {
  long long adj, next, w, valid;
} edge[2 * 410000];
long long gh[410000], n, k, w[410000], top, maxdist, sizz[410000], son[410000];
void addedge(long long x, long long y, long long w) {
  edge[++top].adj = y;
  edge[top].valid = 1;
  edge[top].w = w;
  edge[top].next = gh[x];
  gh[x] = top;
}
void get_size(long long x, long long root = 0) {
  sizz[x] = 1;
  son[x] = 0;
  long long dd = 0;
  for (long long p = gh[x]; p; p = edge[p].next)
    if (edge[p].adj != root && edge[p].valid) {
      get_size(edge[p].adj, x);
      sizz[x] += sizz[edge[p].adj];
      if (sizz[edge[p].adj] > dd) {
        dd = sizz[edge[p].adj];
        son[x] = edge[p].adj;
      }
    }
}
long long getroot(long long x) {
  get_size(x);
  long long sz = sizz[x];
  while (sizz[son[x]] > sz / 2) x = son[x];
  return x;
}
vector<pair<long long, long long> > q[410000][2];
void dfs(long long x, long long pre, long long prec, long long sum,
         long long cnt, long long typ, long long root) {
  if (cnt > k) return;
  update(sum, w[x]);
  q[root][typ].push_back(make_pair(sum, cnt));
  for (long long p = gh[x]; p; p = edge[p].next) {
    if (edge[p].valid == 0) continue;
    if (edge[p].adj == pre) continue;
    dfs(edge[p].adj, x, edge[p].w, sum, cnt + (edge[p].w != prec), typ, root);
  }
}
void dc(long long x) {
  x = getroot(x);
  static long long list[410000], ltop;
  ltop = 0;
  for (long long p = gh[x]; p; p = edge[p].next)
    if (edge[p].valid) list[++ltop] = edge[p].adj;
  for (long long p = gh[x]; p; p = edge[p].next) {
    if (edge[p].valid == 0) continue;
    q[edge[p].adj][0].clear();
    q[edge[p].adj][1].clear();
    dfs(edge[p].adj, x, edge[p].w, 0, 0, edge[p].w, edge[p].adj);
    for (auto t : q[edge[p].adj][0]) update(ans, t.first + w[x]);
    for (auto t : q[edge[p].adj][1]) update(ans, t.first + w[x]);
  }
  update(ans, w[x]);
  for (long long t = 0; t <= 1; t++) {
    if (t == 1) reverse(list + 1, list + ltop + 1);
    del.clear();
    for (long long i = 1; i <= ltop; i++) {
      long long delta = 0;
      if (t == 0) delta = w[x];
      for (auto p : q[list[i]][0])
        update(ans, (p.first + delta) *
                        (get(0, k - p.second) + get(1, k - p.second - 1)) %
                        1000000007);
      for (auto p : q[list[i]][1])
        update(ans, (p.first + delta) *
                        (get(1, k - p.second) + get(0, k - p.second - 1)) %
                        1000000007);
      for (auto p : q[list[i]][0]) insert(0, p.second);
      for (auto p : q[list[i]][1]) insert(1, p.second);
    }
    for (auto p : del) tree[0][p] = tree[1][p] = 0;
  }
  for (long long p = gh[x]; p; p = edge[p].next)
    if (edge[p].valid) {
      edge[p].valid = 0;
      edge[p ^ 1].valid = 0;
      dc(edge[p].adj);
    }
}
signed main() {
  cin >> n >> k;
  for (long long i = 1; i <= n; i++) scanf("%lld", &w[i]);
  top = 1;
  for (long long i = 1; i < n; i++) {
    long long x, y, w;
    scanf("%lld%lld%lld", &x, &y, &w);
    addedge(x, y, w);
    addedge(y, x, w);
  }
  dc(1);
  cout << ans << endl;
  return 0;
}

```