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 maxn = 2e5;
int father[maxn + 5], sz[maxn + 5];
long long res[maxn + 5];
int n, m;
long long ans = 0;
struct Eg {
  int u, v, w;
} E[maxn + 5];
bool cmpe(Eg a, Eg b) { return a.w < b.w; }
long long C2(int x) { return 1LL * x * (x - 1) / 2; }
int _find(int x) {
  if (x == father[x]) return x;
  father[x] = _find(father[x]);
  return father[x];
}
void _merge(int u, int v) {
  u = _find(u);
  v = _find(v);
  if (sz[u] > sz[v]) swap(u, v);
  ans -= C2(sz[u]);
  ans -= C2(sz[v]);
  sz[v] += sz[u];
  father[u] = v;
  ans += C2(sz[v]);
}
struct query {
  int id, up;
} q[maxn + 5];
bool cmp1(query a, query b) { return a.up < b.up; }
int main() {
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= n; i++) {
    father[i] = i;
    sz[i] = 1;
  }
  for (int i = 1; i < n; i++) scanf("%d%d%d", &E[i].u, &E[i].v, &E[i].w);
  sort(E + 1, E + n, cmpe);
  ans = 0;
  for (int i = 1; i <= m; i++) {
    scanf("%d", &q[i].up);
    q[i].id = i;
  }
  sort(q + 1, q + m + 1, cmp1);
  int cur = 1;
  for (int i = 1; i <= m; i++) {
    while (cur <= n - 1 && E[cur].w <= q[i].up) {
      _merge(E[cur].u, E[cur].v);
      cur++;
    }
    res[q[i].id] = ans;
  }
  for (int i = 1; i <= m; i++) printf("%I64d ", res[i]);
  return 0;
}