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:
//package prac;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class R221D {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		int n = ni(), Q = ni();
		a = na(n);
		int[] from = new int[n-1];
		int[] to = new int[n-1];
		for(int i = 0;i < n-1;i++){
			from[i] = ni()-1;
			to[i] = ni()-1;
		}
		int[][] g = packU(n, from, to);
		int[][] pars = parents3(g, 0);
		int[] par = pars[0], ord = pars[1];
		int[] des = new int[n];
		Arrays.fill(des, 1);
		for(int i = n-1;i >= 1;i--){
			int cur = ord[i];
			des[par[cur]] += des[cur];
		}
		int[][] qs = new int[Q][];
		for(int i = 0;i < Q;i++){
			qs[i] = new int[]{ni()-1, ni(), i};
		}
		bucket = makeBuckets(qs, 0, n);
		ans = new int[Q];
		Arrays.fill(ans, -1);
		ft = new int[100055];
		f = new int[100005];
		addFenwick(ft, O, 100000);
		dfs(0, -1, g, false, des);
		for(int v : ans){
			out.println(v);
		}
	}
	
	int[] a;
	int[][][] bucket;
	int[] ans;
	int[] ft;
	int[] f;
	int O = 100005;
	
	public void dfs(int cur, int pre, int[][] g, boolean preserve, int[] des)
	{
		int big = -1;
		for(int e : g[cur]){
			if(e == pre)continue;
			if(big == -1 || des[e] > des[big]){
				big = e;
			}
		}
		for(int e : g[cur]){
			if(e != pre && e != big)dfs(e, cur, g, false, des);
		}
		if(big != -1)dfs(big, cur, g, true, des);
		
		// only biggest subtree is painted
		
		// paint subtrees
		paint(cur);
		// if processing node pairs, put answer(cur);
		for(int e : g[cur]){
			if(e != pre && e != big){
				// if processing node pairs, put answerdfs(e, cur, g);
				paintdfs(e, cur, g);
			}
		}
		
		// all node is painted
		answer(cur);
		
		// clear subtrees
		if(!preserve)cleardfs(cur, pre, g);
	}
	
	private void answer(int cur)
	{
		for(int[] q : bucket[cur]){
			ans[q[2]] = sumFenwick(ft, O-q[1]);
		}
	}
	
	private void paint(int cur)
	{
		addFenwick(ft, O-f[a[cur]], -1);
		f[a[cur]]++;
		addFenwick(ft, O-f[a[cur]], 1);
	}
	
	private void clear(int cur)
	{
		addFenwick(ft, O-f[a[cur]], -1);
		f[a[cur]]--;
		addFenwick(ft, O-f[a[cur]], 1);
	}
	
	private void paintdfs(int cur, int pre, int[][] g)
	{
		paint(cur);
		for(int e : g[cur])if(e != pre)paintdfs(e, cur, g);
	}
	
	private void cleardfs(int cur, int pre, int[][] g)
	{
		clear(cur);
		for(int e : g[cur])if(e != pre)cleardfs(e, cur, g);
	}
	
	private void answerdfs(int cur, int pre, int[][] g)
	{
		answer(cur);
		for(int e : g[cur])if(e != pre)answerdfs(e, cur, g);
	}
	
	public static int sumFenwick(int[] ft, int i)
	{
		int sum = 0;
		for(i++;i > 0;i -= i&-i)sum += ft[i];
		return sum;
	}
	
	public static void addFenwick(int[] ft, int i, int v)
	{
		if(v == 0 || i < 0)return;
		int n = ft.length;
		for(i++;i < n;i += i&-i)ft[i] += v;
	}
	
	
	public static int[][][] makeBuckets(int[][] a, int ind, int sup)
	{
		int n = a.length;
		int[][][] bucket = new int[sup+1][][];
		int[] bp = new int[sup+1];
		for(int i = 0;i < n;i++)bp[a[i][ind]]++;
		for(int i = 0;i <= sup;i++)bucket[i] = new int[bp[i]][];
		for(int i = n-1;i >= 0;i--)bucket[a[i][ind]][--bp[a[i][ind]]] = a[i];
		return bucket;
	}
	
	public static int[][] parents3(int[][] g, int root) {
		int n = g.length;
		int[] par = new int[n];
		Arrays.fill(par, -1);

		int[] depth = new int[n];
		depth[0] = 0;

		int[] q = new int[n];
		q[0] = root;
		for (int p = 0, r = 1; p < r; p++) {
			int cur = q[p];
			for (int nex : g[cur]) {
				if (par[cur] != nex) {
					q[r++] = nex;
					par[nex] = cur;
					depth[nex] = depth[cur] + 1;
				}
			}
		}
		return new int[][] { par, q, depth };
	}

	
	static int[][] packU(int n, int[] from, int[] to) {
		int[][] g = new int[n][];
		int[] p = new int[n];
		for (int f : from)
			p[f]++;
		for (int t : to)
			p[t]++;
		for (int i = 0; i < n; i++)
			g[i] = new int[p[i]];
		for (int i = 0; i < from.length; i++) {
			g[from[i]][--p[from[i]]] = to[i];
			g[to[i]][--p[to[i]]] = from[i];
		}
		return g;
	}
	
	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new R221D().run(); }
	
	private byte[] inbuf = new byte[1024];
	private int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}