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 int link[200005], si[200005];
long long int ans[200005];
vector<pair<long long int, long long int>> v1;
int par(int x) {
  while (link[x] != x) x = link[x];
  return x;
}
void merge(int u, int v, int edge) {
  int pu = par(u);
  int pv = par(v);
  if (si[pu] < si[pv]) {
    ans[edge] += (si[pu] * si[pv]);
    si[pv] += si[pu], link[pu] = pv;
  } else {
    ans[edge] += (si[pu] * si[pv]);
    si[pu] += si[pv], link[pv] = pu;
  }
}
int main() {
  int n, m;
  cin >> n >> m;
  vector<pair<int, pair<int, int>>> ed;
  int mx = 0;
  for (int i = 0; i < n - 1; i++) {
    int u, v, w;
    cin >> u >> v >> w;
    ed.push_back({w, {u, v}});
    mx = max(mx, w);
  }
  sort(ed.begin(), ed.end());
  for (int i = 1; i <= mx; i++) ans[i] = 0;
  for (int i = 1; i <= n; i++) link[i] = i, si[i] = 1;
  int i = 0;
  while (i < n - 1) {
    if (par(ed[i].second.first) != par(ed[i].second.second)) {
      merge(ed[i].second.first, ed[i].second.second, ed[i].first);
    }
    i++;
  }
  long long int sum = 0;
  for (int i = 1; i <= mx; i++) {
    sum += ans[i];
    ans[i] = sum;
  }
  for (int i = 0; i < m; i++) {
    int q;
    cin >> q;
    if (q > mx)
      cout << sum << " ";
    else
      cout << ans[q] << " ";
  }
  cout << endl;
}