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 = 2e3 + 10, inf = 1e9 + 7;
int n, k;
int a[N], dp[N][N], sz[N], tmp[N];
vector<int> adj[N];
void dfs(int u, int prnt = -1) {
  sz[u] = 1;
  dp[u][0] = a[u];
  for (auto v : adj[u]) {
    if (v != prnt) {
      dfs(v, u);
      int nw = max(sz[u], sz[v] + 1);
      for (int i = 0; i < nw; i++) tmp[i] = -inf;
      for (int i = 0; i < sz[u]; i++) {
        for (int j = max(0, k - i); j < sz[v]; ++j)
          tmp[min(i, j + 1)] = max(tmp[min(i, j + 1)], dp[u][i] + dp[v][j]);
      }
      for (int i = 0; i < sz[v]; i++) tmp[i + 1] = max(tmp[i + 1], dp[v][i]);
      for (int i = 0; i < sz[u]; i++) dp[u][i] = max(dp[u][i], tmp[i]);
      for (int i = sz[u]; i < nw; ++i) dp[u][i] = tmp[i];
      sz[u] = nw;
      for (int i = sz[u] - 1; i > 0; --i)
        dp[u][i - 1] = max(dp[u][i - 1], dp[u][i]);
    }
  }
}
int main() {
  cin >> n >> k;
  for (int i = 0; i < n; i++) cin >> a[i];
  for (int i = 0; i < n - 1; i++) {
    int u, v;
    cin >> u >> v;
    adj[u - 1].push_back(v - 1);
    adj[v - 1].push_back(u - 1);
  }
  dfs(0);
  cout << dp[0][0];
}