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;
vector<int64_t> parent;
int64_t getComponent(int64_t pos) {
  if (parent[pos] != pos) {
    parent[pos] = getComponent(parent[pos]);
  }
  return parent[pos];
}
signed main() {
  int64_t n, queries;
  cin >> n >> queries;
  parent.assign(n, -1);
  iota(parent.begin(), parent.end(), 0);
  vector<tuple<int64_t, int64_t, int64_t>> edges(n - 1);
  vector<int64_t> componentSize(n, 1);
  for (auto& [cost, start, end] : edges) {
    cin >> start >> end >> cost;
    start--;
    end--;
  }
  sort(edges.begin(), edges.end());
  map<int64_t, int64_t> results;
  auto numCombinations = [](int64_t n) { return n * (n - 1) / 2; };
  int64_t previousResult = 0;
  results[0] = 0;
  for (auto& [cost, start, end] : edges) {
    int64_t startSize = componentSize[getComponent(start)];
    int64_t endSize = componentSize[getComponent(end)];
    results[cost] = previousResult =
        previousResult - numCombinations(startSize) - numCombinations(endSize) +
        numCombinations(startSize + endSize);
    parent[getComponent(start)] = end;
    componentSize[getComponent(start)] = startSize + endSize;
  }
  for (int64_t t = 0; t < queries; t++) {
    int64_t q;
    cin >> q;
    cout << prev(results.upper_bound(q))->second << " ";
  }
  cout << endl;
}