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;
vector<long long> parent, size;
struct dsu {
  void init(long long n) {
    size.resize(n, 1);
    parent.resize(n);
    for (long long i = 0; i <= n - 1; i++) parent[i] = i;
  }
  long long get_superparent(long long i) {
    if (parent[i] == i) return i;
    return parent[i] = get_superparent(parent[i]);
  }
  long long unite(long long x, long long y) {
    long long s1 = get_superparent(x), s2 = get_superparent(y);
    if (s1 != s2) {
      parent[s2] = s1;
      long long cnt = size[s1] * size[s2];
      size[s1] += size[s2];
      return cnt;
    }
    return 0;
  }
};
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long t;
  t = 1;
  while (t--) {
    long long n, m;
    cin >> n >> m;
    vector<pair<long long, pair<long long, long long>>> edges;
    for (long long i = 0; i <= n - 2; i++) {
      long long x, y, w;
      cin >> x >> y >> w;
      x--;
      y--;
      edges.push_back({w, {x, y}});
    }
    sort(edges.begin(), edges.end());
    dsu g;
    g.init(n);
    map<long long, long long> cntmp;
    for (long long i = 0; i <= n - 2; i++) {
      long long x = edges[i].second.first, y = edges[i].second.second,
                w = edges[i].first;
      cntmp[w] += g.unite(x, y);
    }
    vector<pair<long long, long long>> cummulative;
    long long prev = 0;
    for (auto w : cntmp) {
      cummulative.push_back({w.first, prev + w.second});
      prev += w.second;
    }
    for (long long i = 1; i <= m; i++) {
      long long q;
      cin >> q;
      pair<long long, long long> temp = {q, 1e15};
      auto it = upper_bound(cummulative.begin(), cummulative.end(), temp);
      if (it == cummulative.begin())
        cout << 0;
      else {
        it--;
        cout << it->second;
      }
      cout << " ";
    }
  }
  return 0;
}