Tree and Queries

1000ms

262144K

Description:

You have a rooted tree consisting of n vertices. Each vertex of the tree has some color. We will assume that the tree vertices are numbered by integers from 1 to n. Then we represent the color of vertex v as c_v. The tree root is a vertex with number 1.

In this problem you need to answer to m queries. Each query is described by two integers v_j, k_j. The answer to query v_j, k_j is the number of such colors of vertices x, that the subtree of vertex v_j contains at least k_j vertices of color x.

You can find the definition of a rooted tree by the following link: http://en.wikipedia.org/wiki/Tree_(graph_theory).

Input:

The first line contains two integers n and m (2 ≤ n ≤ 10⁵; 1 ≤ m ≤ 10⁵). The next line contains a sequence of integers c₁, c₂, ..., c_n (1 ≤ c_i ≤ 10⁵). The next n - 1 lines contain the edges of the tree. The i-th line contains the numbers a_i, b_i (1 ≤ a_i, b_i ≤ n; a_i ≠ b_i) — the vertices connected by an edge of the tree.

Next m lines contain the queries. The j-th line contains two integers v_j, k_j (1 ≤ v_j ≤ n; 1 ≤ k_j ≤ 10⁵).

Output:

Print m integers — the answers to the queries in the order the queries appear in the input.

Sample Input:

8 5
1 2 2 3 3 2 3 3
1 2
1 5
2 3
2 4
5 6
5 7
5 8
1 2
1 3
1 4
2 3
5 3

Sample Output:

Sample Input:

Sample Output:

Note:

A subtree of vertex v in a rooted tree with root r is a set of vertices {u : dist(r, v) + dist(v, u) = dist(r, u)}. Where dist(x, y) is the length (in edges) of the shortest path between vertices x and y.

Informação

Provedor Codeforces

Código CF375D