Problem: You are given a weighted tree consisting of n vertices. Recall that a tree is a connected graph without cycles. Vertices u_i and v_i are connected by an edge with weight w_i.

You are given m queries. The i-th query is given as an integer q_i. In this query you need to calculate the number of pairs of vertices (u, v) (u < v) such that the maximum weight of an edge on a simple path between u and v doesn't exceed q_i.

Input

The first line of the input contains two integers n and m (1 ≤ n, m ≤ 2 ⋅ 10^5) — the number of vertices in the tree and the number of queries.

Each of the next n - 1 lines describes an edge of the tree. Edge i is denoted by three integers u_i, v_i and w_i — the labels of vertices it connects (1 ≤ u_i, v_i ≤ n, u_i ≠ v_i) and the weight of the edge (1 ≤ w_i ≤ 2 ⋅ 10^5). It is guaranteed that the given edges form a tree.

The last line of the input contains m integers q_1, q_2, ..., q_m (1 ≤ q_i ≤ 2 ⋅ 10^5), where q_i is the maximum weight of an edge in the i-th query.

Output

Print m integers — the answers to the queries. The i-th value should be equal to the number of pairs of vertices (u, v) (u < v) such that the maximum weight of an edge on a simple path between u and v doesn't exceed q_i.

Queries are numbered from 1 to m in the order of the input.

Examples

Input


7 5
1 2 1
3 2 3
2 4 1
4 5 2
5 7 4
3 6 2
5 2 3 4 1


Output


21 7 15 21 3 


Input


1 2
1 2


Output


0 0 


Input


3 3
1 2 1
2 3 2
1 3 2


Output


1 3 3 

Note

The picture shows the tree from the first example: <image>

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
long long p[200005];
long long baap(long long x) {
  if (x == p[x]) return x;
  return p[x] = baap(p[x]);
}
long long calc(long long x) { return (x * (x - 1)) / 2; }
int main() {
  long long n, m, a, b, c;
  cin >> n >> m;
  vector<pair<long long, pair<long long, long long> > > v;
  long long wt[n + 2];
  for (int i = 0; i <= n; i++) {
    p[i] = i;
    wt[i] = 1;
  }
  for (int i = 0; i < n - 1; i++) {
    cin >> a >> b >> c;
    --a;
    --b;
    v.push_back({c, {a, b}});
  }
  vector<pair<long long, long long> > q;
  for (int i = 0; i < m; i++) {
    cin >> a;
    q.push_back({a, i});
  }
  long long ind = 0, vl = 0, ans[m + 1];
  sort(v.begin(), v.end());
  sort(q.begin(), q.end());
  for (int i = 0; i < m; i++) {
    while (ind < n - 1 && q[i].first >= v[ind].first) {
      long long x = v[ind].second.first;
      long long y = v[ind].second.second;
      x = baap(x);
      y = baap(y);
      if (wt[x] < wt[y]) swap(x, y);
      vl -= calc(wt[x]);
      vl -= calc(wt[y]);
      wt[x] += wt[y];
      vl += calc(wt[x]);
      p[y] = x;
      ind++;
    }
    ans[q[i].second] = vl;
  }
  for (int i = 0; i < m; i++) cout << ans[i] << " ";
  return 0;
}