Problem: 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 cv. 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 vj, kj. The answer to query vj, kj is the number of such colors of vertices x, that the subtree of vertex vj contains at least kj 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, ..., cn (1 ≤ ci ≤ 105). The next n - 1 lines contain the edges of the tree. The i-th line contains the numbers ai, bi (1 ≤ ai, bi ≤ n; ai ≠ bi) — the vertices connected by an edge of the tree.

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

Output

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

Examples

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


Output

2
2
1
0
1


Input

4 1
1 2 3 4
1 2
2 3
3 4
1 1


Output

4

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.

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;


//11:38
public class D221 {
    static int N, Q,count=0;
    static int[] color,dfs,l,r;
    public static void main(String[] args) {
        
        
        FS scan = new FS(System.in);
        
        N = scan.nextInt();
        Q = scan.nextInt();
        color = new int[N];
        dfs = new int[2*N];
        l = new int[N];
        r = new int[N];
        
        ArrayList<Integer>[] adj = new ArrayList[N];
        for(int i=0;i<N;i++)color[i] = scan.nextInt();
        for(int i=0;i<N;i++)adj[i] = new ArrayList<>();
        for(int i=0;i<N-1;i++){
            int u = scan.nextInt()-1, v = scan.nextInt()-1;
            adj[u].add(v);
            adj[v].add(u);
        }
        
        dfs(0,-1,adj);
        
        int SQRT = (int)Math.ceil(Math.sqrt(2*N));
        
        Query[] list = new Query[Q];
        
        for(int q=0;q<Q;q++){
            int node = scan.nextInt()-1, v = scan.nextInt();
            list[q] = new Query(l[node],r[node],v,q);
        }
        Arrays.sort(list);
        
        int[] count = new int[100001];
        int[] size = new int[200001];
        for(Query q : list) {
            int b1 = q.l/SQRT, b2 = q.r/SQRT;
            if(b1!=b2)continue;
            
            
            for( int i=q.l;i<=q.r;i++){
                add(color[dfs[i]],count,size);
            }
            q.sol = size[q.v*2];
            for( int i=q.l;i<=q.r;i++){
                sub(color[dfs[i]],count,size);
            }
          
        }
        
        int l=1,r=0;
        for(Query q : list) {
            if(q.sol!=-1)continue;
            if(r<q.r){
                for(int i=l;i<=r;i++)sub(color[dfs[i]],count,size);
                l = q.l;
                r = q.r;
                for( int i=l;i<=r;i++)add(color[dfs[i]],count,size);
            }
            while(q.l>l){
                sub(color[dfs[l]],count,size);
                l++;
            }
            while(q.r<r){
                sub(color[dfs[r]],count,size);
                r--;
            }
           
            q.sol = size[q.v*2];
        }
        
        int[] sol = new int[Q];
        
        for(Query q : list) {
            sol[q.idx] = q.sol;
        }
        PrintWriter out = new PrintWriter(System.out);
        for(int i=0;i<Q;i++){
            out.println(sol[i]);
        }
        out.close();
    }
    
    private static void add(int color, int[] count ,int[] size) {
        size[++count[color]]++;
    }
    private static void sub(int color, int[] count, int[] size) {
        size[count[color]--]--;
    }
    
    private static class Query implements Comparable<Query>{
        int l, r, v,idx, sol = -1;
        public Query(int l, int r, int v, int idx) {
            this.l=l;
            this.r=r;
            this.v=v;
            this.idx=idx;
        }
        public int compareTo(Query a) {
            return Integer.compare(this.l, a.l);
        }
    }
    private static void dfs(int idx, int prev, ArrayList<Integer>[] adj) {
        
        l[idx] = count;
        dfs[count++]=idx;
        for(int i : adj[idx]){
            if(i==prev)continue;
            dfs(i,idx,adj); 
        }
        r[idx] = count;
        dfs[count++]=idx;
    }
    private static class FS {
        BufferedReader br;
        StringTokenizer st;
        public FS(InputStream in) {
            br = new BufferedReader(new InputStreamReader(in));
        }
        String next(){
            while(st==null||!st.hasMoreElements()){
                try{st = new StringTokenizer(br.readLine());}
                catch(IOException e){e.printStackTrace();}
            }
            return st.nextToken();
        }
        int nextInt() {return Integer.parseInt(next());}
        long nextLong() {return Long.parseLong(next());}
        double nextDouble() { return Double.parseDouble(next());}
    }
}