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.*;
import java.util.*;

public class CF {

	int[] color;
	ArrayList<Integer>[] g;
	int[] ans;
	ArrayList<Ask>[] q;

	class Ask {
		int id, cnt;

		Ask(int id, int cnt) {
			this.id = id;
			this.cnt = cnt;
		}
	}

	class Vertex {
		HashMap<Integer, Integer> hm;
		ArrayList<Integer> ans;

		Vertex() {
			hm = new HashMap<>(1);
			ans = new ArrayList<>(1);
		}
	}

	void update(ArrayList<Integer> arr, int from, int to) {
		for (int i = from; i <= to; i++) {
			while (arr.size() <= i)
				arr.add(0);
			arr.set(i, arr.get(i) + 1);
		}
	}

	Vertex union(Vertex v1, Vertex v2) {
		if (v1.hm.size() < v2.hm.size())
			return union(v2, v1);
		for (Map.Entry<Integer, Integer> entry : v2.hm.entrySet()) {
			Integer was = v1.hm.get(entry.getKey());
			if (was == null)
				was = 0;
			update(v1.ans, was + 1, was + entry.getValue());
			v1.hm.put(entry.getKey(), entry.getValue() + was);
		}
		return v1;
	}

	int get(ArrayList<Integer> x, int pos) {
		return pos >= x.size() ? 0 : x.get(pos);
	}

	Vertex go(int v, int p) {
		Vertex res = new Vertex();
		update(res.ans, 0, 1);
		res.hm.put(color[v], 1);
		for (int i = 0; i < g[v].size(); i++) {
			int to = g[v].get(i);
			if (to == p)
				continue;
			Vertex xx = go(to, v);
			res = union(res, xx);
		}
		for (int i = 0; i < q[v].size(); i++) {
			ans[q[v].get(i).id] = get(res.ans, q[v].get(i).cnt);
		}
		return res;
	}

	void solve() {
		int n = in.nextInt();
		int m = in.nextInt();
		color = new int[n];
		for (int i = 0; i < n; i++)
			color[i] = in.nextInt() - 1;
		g = new ArrayList[n];
		for (int i = 0; i < n; i++)
			g[i] = new ArrayList<>();
		for (int i = 0; i < n - 1; i++) {
			int fr = in.nextInt() - 1;
			int to = in.nextInt() - 1;
			g[fr].add(to);
			g[to].add(fr);
		}
		ans = new int[m];
		q = new ArrayList[n];
		for (int i = 0; i < n; i++) {
			q[i] = new ArrayList<>();
		}
		for (int i = 0; i < m; i++) {
			int v = in.nextInt() - 1;
			int how = in.nextInt();
			q[v].add(new Ask(i, how));
		}
		go(0, -1);
		for (int i = 0; i < m; i++)
			out.println(ans[i]);
	}

	FastScaner in;
	PrintWriter out;

	void run() {
		in = new FastScaner(System.in);
		out = new PrintWriter(System.out);

		solve();

		out.close();
	}

	void runWithFiles() {
		in = new FastScaner(new File("input.txt"));
		try {
			out = new PrintWriter(new File("output.txt"));
		} catch (FileNotFoundException e) {
			e.printStackTrace();
		}

		solve();

		out.close();
	}

	public static void main(String[] args) {
		Locale.setDefault(Locale.US);
		new CF().run();
	}

	class FastScaner {
		BufferedReader br;
		StringTokenizer st;

		FastScaner(InputStream is) {
			br = new BufferedReader(new InputStreamReader(is));
		}

		FastScaner(File f) {
			try {
				br = new BufferedReader(new FileReader(f));
			} catch (FileNotFoundException e) {
				e.printStackTrace();
			}
		}

		String next() {
			while (st == null || !st.hasMoreElements()) {
				String s = null;
				try {
					s = br.readLine();
				} catch (IOException e) {
					e.printStackTrace();
				}
				if (s == null)
					return null;
				st = new StringTokenizer(s);
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}
	}
}