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;
using ull = unsigned long long;
using ll = long long;
const int N = 205, MOD = 1e9 + 7;
int n, k, a[N], dp[N][N];
vector<int> g[N];
void dfs(int u, int p = -1) {
  for (auto v : g[u]) {
    if (v != p) {
      dfs(v, u);
    }
  }
  dp[u][0] = a[u];
  for (auto v : g[u]) {
    if (dp[v][k - 1] != -(int)2e9) {
      dp[u][0] += dp[v][k - 1];
    }
  }
  for (int j = 1; j <= k; ++j) {
    int sm = 0, dt = max(j, k - j);
    vector<int> vv, vec;
    for (auto v : g[u]) {
      if (v != p) {
        if (dp[v][dt - 1] != -(int)2e9) {
          sm += dp[v][dt - 1];
          vv.push_back(dp[v][dt - 1]), vec.push_back(dp[v][j - 1]);
        }
      }
    }
    dp[u][j] = sm;
    int sz = (int)vv.size();
    for (int l = 0; l < sz; ++l) {
      if (vec[l] != -(int)2e9) {
        dp[u][j] = max(dp[u][j], sm - vv[l] + vec[l]);
      }
    }
  }
  for (int j = k - 1; j >= 0; --j) {
    dp[u][j] = max(dp[u][j], dp[u][j + 1]);
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0), cout.tie(0);
  cin >> n >> k;
  for (int i = 1; i <= n; ++i) {
    cin >> a[i];
    fill(dp[i], dp[i] + N, -(int)2e9);
  }
  for (int i = 0, u, v; i < n - 1; ++i) {
    cin >> u >> v;
    g[u].push_back(v), g[v].push_back(u);
  }
  ++k;
  dfs(1);
  cout << dp[1][0] << '\n';
  return 0;
}