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 + 5;
long long ans = 0, parent[N], compSize[N];
deque<pair<int, pair<int, int> > > edges;
map<int, long long> mop;
int arr[N], sorted[N];
int getParent(int node) {
  if (parent[node] == node) return node;
  return parent[node] = getParent(parent[node]);
}
void connect(int u, int v) {
  if (getParent(u) != getParent(v)) {
    ans -= (compSize[getParent(u)] * (compSize[getParent(u)] - 1)) / 2;
    ans -= (compSize[getParent(v)] * (compSize[getParent(v)] - 1)) / 2;
    compSize[getParent(v)] += compSize[parent[u]];
    parent[getParent(u)] = getParent(v);
    ans += (compSize[getParent(v)] * (compSize[getParent(v)] - 1)) / 2;
  }
}
int main() {
  int n, m;
  cin >> n >> m;
  for (int i = 0; i <= n; i++) compSize[i] = 1, parent[i] = i;
  for (int i = 0; i < n - 1; i++) {
    int u, v, w;
    cin >> u >> v >> w;
    edges.push_back({w, {u, v}});
  }
  sort(edges.begin(), edges.end());
  for (int i = 0; i < m; i++) {
    cin >> arr[i];
    sorted[i] = arr[i];
  }
  sort(sorted, sorted + m);
  for (int i = 0; i < m; i++) {
    while (edges.size() and edges.front().first <= sorted[i]) {
      connect(edges.front().second.first, edges.front().second.second);
      edges.pop_front();
    }
    mop[sorted[i]] = ans;
  }
  for (int i = 0; i < m; i++) cout << mop[arr[i]] << " ";
}