G. Path Queriestime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.InputThe first line of the input contains two integers n and m (1 \le n, m \le 2 \cdot 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 \le u_i, v_i \le n, u_i \ne v_i) and the weight of the edge (1 \le w_i \le 2 \cdot 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, \dots, q_m (1 \le q_i \le 2 \cdot 10^5), where q_i is the maximum weight of an edge in the i-th query.OutputPrint 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.ExamplesInput
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 
NoteThe picture shows the tree from the first example: 
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

21 7 15 21 3  
['divide and conquer', 'dsu', 'graphs', 'sortings', 'trees', '*1800']