## 题目描述

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

$v_{j},k_{j}$

$v_{j},k_{j}$

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).

## 输入输出格式

The first line contains two integers

$n$

and

$m$

$(2<=n<=10^{5}; 1<=m<=10^{5})$ . The next line contains a sequence of integers

$c_{1},c_{2},…,c_{n}$

$(1<=c_{i}<=10^{5})$

. 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

$v_{j},k_{j}$

$(1<=v_{j}<=n; 1<=k_{j}<=10^{5})$ .

Print

$m$

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

## 说明

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

$y$

.