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;
const int N = 1e6 + 100;
int par[N];
int sz[N];
long long all_path;
int P(int u) {
  if (par[u] == u) return u;
  return par[u] = P(par[u]);
}
void Merge(int u, int v) {
  u = P(u);
  v = P(v);
  par[v] = u;
  all_path += 1ll * sz[u] * sz[v];
  sz[u] += sz[v];
}
long long res[N];
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int n, q;
  cin >> n >> q;
  for (int i = 1; i <= n; i++) par[i] = i, sz[i] = 1;
  vector<tuple<int, int, int>> edges;
  for (int i = 1; i < n; i++) {
    int u, v, w;
    cin >> u >> v >> w;
    edges.push_back(make_tuple(w, u, v));
  }
  sort(edges.begin(), edges.end());
  reverse(edges.begin(), edges.end());
  vector<pair<int, int>> offline_queries;
  for (int i = 1; i <= q; i++) {
    int w;
    cin >> w;
    offline_queries.push_back({w, i});
  }
  sort(offline_queries.begin(), offline_queries.end());
  for (int i = 0; i < q; i++) {
    int w = offline_queries[i].first, idx = offline_queries[i].second;
    while (edges.size() > 0 && get<0>(edges.back()) <= w) {
      int u = get<1>(edges.back()), v = get<2>(edges.back());
      edges.pop_back();
      Merge(u, v);
    }
    res[idx] = all_path;
  }
  for (int i = 1; i <= q; i++) {
    cout << res[i] << " ";
  }
}