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;
string to_string(string s) { return '"' + s + '"'; }
string to_string(const char* s) { return to_string((string)s); }
string to_string(bool b) { return (b ? "true" : "false"); }
template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <typename A>
string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto& x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}
const long long int N = 200005;
set<pair<long long int, pair<long long int, long long int>>> st;
long long int cnt[N];
long long int dsu[N];
long long int root(long long int x) {
  while (x != dsu[x]) {
    dsu[x] = dsu[dsu[x]];
    x = dsu[x];
  }
  return x;
}
void union_(long long int x, long long int y) {
  x = root(x);
  y = root(y);
  dsu[x] = y;
}
signed main() {
  std::ios::sync_with_stdio(false);
  for (long long int i = 0; i < N; i++) dsu[i] = i, cnt[i] = 1;
  long long int n, q;
  cin >> n >> q;
  st.clear();
  map<long long int, long long int> mp;
  mp[0] = 0;
  for (long long int i = 1; i < n; i++) {
    long long int x, y, w;
    cin >> x >> y >> w;
    st.insert({w, {x, y}});
  }
  long long int ans = 0;
  for (auto i : st) {
    long long int x = i.second.first;
    long long int y = i.second.second;
    long long int w = i.first;
    ans += cnt[root(x)] * cnt[root(y)];
    cnt[root(y)] += cnt[root(x)];
    union_(x, y);
    mp[w] = ans;
  }
  while (q--) {
    long long int qi;
    cin >> qi;
    auto itr = mp.upper_bound(qi);
    itr = prev(itr);
    cout << itr->second << " ";
  }
}