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 = 2e5 + 10;
struct tp {
  int u, v, w;
};
int n, m, id;
int r[N], tree_size[N];
tp edge[N];
pair<int, int> queries[N];
pair<long long, int> res[N];
bool cmp(pair<long long, int> a, pair<long long, int> b) {
  return a.second < b.second;
}
int root(int u) {
  if (u != r[u]) return r[u] = root(r[u]);
  return u;
}
bool cmptp(tp a, tp b) { return a.w < b.w; }
int main() {
  int u, v, w, ru, rv;
  cin >> n >> m;
  for (int i = 1; i <= n; i++) tree_size[i] = 1, r[i] = i;
  for (int i = 1; i < n; i++) cin >> edge[i].u >> edge[i].v >> edge[i].w;
  sort(edge + 1, edge + n, cmptp);
  for (int i = 1; i <= m; i++) {
    cin >> queries[i].first;
    queries[i].second = i;
  }
  sort(queries + 1, queries + 1 + m);
  for (int i = 1; i <= m; i++) res[i].second = queries[i].second;
  id = 1;
  for (int i = 1; i < n; i++) {
    u = edge[i].u, v = edge[i].v, w = edge[i].w;
    ru = root(u), rv = root(v);
    while (w > queries[id].first && id <= m) {
      id += (id <= m);
      res[id].first += res[id - 1].first;
    }
    res[id].first += 1ll * tree_size[ru] * tree_size[rv];
    r[ru] = rv;
    tree_size[rv] += tree_size[ru];
  }
  while (id <= m) {
    id++;
    res[id].first += res[id - 1].first;
  }
  sort(res + 1, res + 1 + m, cmp);
  for (int i = 1; i <= m; i++) cout << res[i].first << " ";
}