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.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Calendar;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.SortedSet;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

/**
 * #
 * 
 * @author pttrung
 */
public class D_Round_211_Div1 {

	public static long MOD = 1000000007;
	static int[] first;
	static int[] last;
	static int cur = 0;

	public static void main(String[] args) throws FileNotFoundException {
		// PrintWriter out = new PrintWriter(new FileOutputStream(new File(
		// "output.txt")));
		PrintWriter out = new PrintWriter(System.out);
		Scanner in = new Scanner();
		int n = in.nextInt();
		int m = in.nextInt();
		int[] data = new int[n];
		first = new int[n];
		last = new int[n];
		ArrayList<Integer>[] map = new ArrayList[n];
		for (int i = 0; i < n; i++) {
			data[i] = in.nextInt();
			map[i] = new ArrayList();
		}
		for (int i = 0; i < n - 1; i++) {
			int a = in.nextInt() - 1;
			int b = in.nextInt() - 1;
			map[a].add(b);
			map[b].add(a);
		}
		int[][] q = new int[m][2];
		for (int i = 0; i < m; i++) {
			q[i][0] = in.nextInt() - 1;
			q[i][1] = in.nextInt();
		}
		int[] store = new int[n];
		dfs(0, 0, data, store, map);

		Q[] query = new Q[m];
		for (int i = 0; i < m; i++) {
			query[i] = new Q(first[q[i][0]], last[q[i][0]], q[i][1], i);
		}
		// System.out.println(Arrays.toString(query));
		int length = (int) Math.max(1, Math.sqrt(cur));
		int total = cur / length;
		if (cur % length != 0) {
			total++;
		}
		ArrayList<Q>[] list = new ArrayList[total];
		Arrays.sort(query, new Comparator<Q>() {

			@Override
			public int compare(Q o1, Q o2) {
				// TODO Auto-generated method stub
				return Integer.compare(o1.b, o2.b);
			}
		});
		int index = 0;
		for (int i = 0; i < list.length; i++) {
			list[i] = new ArrayList();
			int max = (i + 1) * length;
			while (index < m && query[index].b < max) {
				list[i].add(query[index++]);
			}
			// System.out.println(max);
			Collections.sort(list[i], new Comparator<Q>() {

				@Override
				public int compare(Q o1, Q o2) {
					if (o1.a != o2.a)
						return Integer.compare(o1.a, o2.a);
					return Integer.compare(o1.b, o2.b);
				}
			});
		}

		int start = 0;
		int end = 0;
		int[] count = new int[100001];
		count[store[0]]++;
		FT tree = new FT(n + 1);
		tree.update(count[store[0]], 1);
		int[] result = new int[m];
		for (ArrayList<Q> tmp : list) {
			for (Q x : tmp) {

				while (x.b < end) {

					count[store[end]]--;
					if (count[store[end]] > 0) {
						tree.update(count[store[end]], 1);
					}
					tree.update(count[store[end]] + 1, -1);
					end--;
				}
				while (x.b > end) {
					end++;
					count[store[end]]++;
					tree.update(count[store[end]], 1);
					if (count[store[end]] > 1) {
						tree.update(count[store[end]] - 1, -1);
					}

				}
				while (x.a > start) {

					count[store[start]]--;
					if (count[store[start]] > 0) {
						tree.update(count[store[start]], 1);
					}
					tree.update(count[store[start]] + 1, -1);
					start++;
				}
				while (x.a < start) {
					start--;
					count[store[start]]++;
					tree.update(count[store[start]], 1);
					if (count[store[start]] > 1) {
						tree.update(count[store[start]] - 1, -1);
					}

				}
				if (x.k <= n) {
					result[x.index] = (int) (tree.get(n) - (x.k > 1 ? tree
							.get(x.k - 1) : 0));
				}
			}
		}
		for (int i : result) {
			out.println(i);
		}

		out.close();
	}

	static class Q {
		int a, b, k, index;

		public Q(int a, int b, int k, int index) {
			super();
			this.a = a;
			this.b = b;
			this.k = k;
			this.index = index;
		}

		@Override
		public String toString() {
			return "Q [a=" + a + ", b=" + b + ", k=" + k + ", index=" + index
					+ "]";
		}

	}

	static void dfs(int index, int pa, int[] data, int[] store,
			ArrayList<Integer>[] map) {
		first[index] = cur;
		store[cur] = data[index];
		cur++;
		for (int i : map[index]) {
			if (i != pa) {
				dfs(i, index, data, store, map);
			}
		}
		last[index] = cur - 1;
	}

	public static int[] KMP(String val) {
		int i = 0;
		int j = -1;
		int[] result = new int[val.length() + 1];
		result[0] = -1;
		while (i < val.length()) {
			while (j >= 0 && val.charAt(j) != val.charAt(i)) {
				j = result[j];
			}
			j++;
			i++;
			result[i] = j;
		}
		return result;

	}

	public static boolean nextPer(int[] data) {
		int i = data.length - 1;
		while (i > 0 && data[i] < data[i - 1]) {
			i--;
		}
		if (i == 0) {
			return false;
		}
		int j = data.length - 1;
		while (data[j] < data[i - 1]) {
			j--;
		}
		int temp = data[i - 1];
		data[i - 1] = data[j];
		data[j] = temp;
		Arrays.sort(data, i, data.length);
		return true;
	}

	public static int digit(long n) {
		int result = 0;
		while (n > 0) {
			n /= 10;
			result++;
		}
		return result;
	}

	public static double dist(long a, long b, long x, long y) {
		double val = (b - a) * (b - a) + (x - y) * (x - y);
		val = Math.sqrt(val);
		double other = x * x + a * a;
		other = Math.sqrt(other);
		return val + other;

	}

	public static class Point implements Comparable<Point> {

		int x, y;

		public Point(int start, int end) {
			this.x = start;
			this.y = end;
		}

		@Override
		public int hashCode() {
			int hash = 5;
			hash = 47 * hash + this.x;
			hash = 47 * hash + this.y;
			return hash;
		}

		@Override
		public boolean equals(Object obj) {
			if (obj == null) {
				return false;
			}
			if (getClass() != obj.getClass()) {
				return false;
			}
			final Point other = (Point) obj;
			if (this.x != other.x) {
				return false;
			}
			if (this.y != other.y) {
				return false;
			}
			return true;
		}

		@Override
		public int compareTo(Point o) {
			return x - o.x;
		}
	}

	public static class FT {

		long[] data;

		FT(int n) {
			data = new long[n];
		}

		public void update(int index, long value) {
			while (index < data.length) {
				data[index] += value;
				index += (index & (-index));
			}
		}

		public long get(int index) {
			long result = 0;
			while (index > 0) {
				result += data[index];
				index -= (index & (-index));
			}
			return result;

		}
	}

	public static long gcd(long a, long b) {
		if (b == 0) {
			return a;
		}
		return gcd(b, a % b);
	}

	public static long pow(long a, long b) {
		if (b == 0) {
			return 1;
		}
		if (b == 1) {
			return a;
		}
		long val = pow(a, b / 2);
		if (b % 2 == 0) {
			return val * val % MOD;
		} else {
			return val * (val * a % MOD) % MOD;

		}
	}

	static class Scanner {

		BufferedReader br;
		StringTokenizer st;

		public Scanner() throws FileNotFoundException {
			// System.setOut(new PrintStream(new
			// BufferedOutputStream(System.out), true));
			br = new BufferedReader(new InputStreamReader(System.in));
			// br = new BufferedReader(new InputStreamReader(new
			// FileInputStream(new File("input.txt"))));
		}

		public String next() {

			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (Exception e) {
					throw new RuntimeException();
				}
			}
			return st.nextToken();
		}

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

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

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

		public String nextLine() {
			st = null;
			try {
				return br.readLine();
			} catch (Exception e) {
				throw new RuntimeException();
			}
		}

		public boolean endLine() {
			try {
				String next = br.readLine();
				while (next != null && next.trim().isEmpty()) {
					next = br.readLine();
				}
				if (next == null) {
					return true;
				}
				st = new StringTokenizer(next);
				return st.hasMoreTokens();
			} catch (Exception e) {
				throw new RuntimeException();
			}
		}
	}
}