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;
void fun() {}
long long int md = 1e9 + 7;
long long int __gcd(long long int a, long long int b) {
  if (b == 0) return a;
  return __gcd(b, a % b);
}
long long int poww(long long int a, long long int b, long long int md) {
  if (b < 0) return 0;
  if (a == 0) return 0;
  long long int res = 1;
  while (b) {
    if (b & 1) {
      res = (1ll * res * a) % md;
    }
    a = (1ll * a * a) % md;
    b >>= 1;
  }
  return res;
}
long long int poww(long long int a, long long int b) {
  if (b < 0) return 0;
  if (a == 0) return 0;
  long long int res = 1;
  while (b) {
    if (b & 1) {
      res = (1ll * res * a);
    }
    a = (1ll * a * a);
    b >>= 1;
  }
  return res;
}
void ainp(long long int arr[], long long int n) {
  for (long long int i = 1; i <= n; i++) cin >> arr[i];
}
void disp(long long int arr[], long long int n) {
  for (long long int i = 1; i <= n; i++) cout << arr[i] << " ";
  cout << "\n";
}
void dispv(vector<long long int> &v) {
  for (long long int i = 0; i < v.size(); i++) cout << v[i] << " ";
  cout << "\n";
}
long long int divide(long long int a, long long int b, long long int md) {
  long long int rr = a * (poww(b, md - 2, md));
  rr %= md;
  return rr;
}
const long long int size = 2e5 + 5;
long long int parent[size], membercount[size], ans[size];
vector<pair<long long int, long long int> > edges[size];
long long int n, u, v, m, w;
long long int ncr(long long int n, long long int r) { return n * (n - 1) / 2; }
long long int findp(long long int par) {
  if (parent[par] == par) return par;
  return parent[par] = findp(parent[par]);
}
long long int unite(long long int par, long long int child) {
  child = findp(child);
  par = findp(par);
  long long int term = ncr(membercount[par], 2) + ncr(membercount[child], 2);
  membercount[par] += membercount[child];
  parent[child] = par;
  return ncr(membercount[par], 2) - term;
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  fun();
  cin >> n >> m;
  for (long long int i = 1; i <= n; i++) parent[i] = i, membercount[i] = 1;
  for (long long int i = 1; i < n; i++) {
    cin >> u >> v >> w;
    edges[w].push_back(make_pair(u, v));
  }
  long long int total = 0;
  for (long long int wt = 0; wt <= 2e5; wt++) {
    for (long long int i = 0; i < edges[wt].size(); i++) {
      total += unite(edges[wt][i].first, edges[wt][i].second);
    }
    ans[wt] = total;
  }
  while (m--) {
    long long int wt;
    cin >> wt;
    cout << ans[wt] << " ";
  }
  cout << "\n";
  return 0;
}