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.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Random;
import java.util.Scanner;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

public class SuffixArray {
	private static InputStream stream;
	private static byte[] buf = new byte[1024];
	private static int curChar;
	private static int numChars;
	private static SpaceCharFilter filter;
	private static PrintWriter pw;
	private static long max = Long.MIN_VALUE;
	private static int mod = 1000000000 + 7;
	private static boolean flag=false;
	private static int block;
	private static void soln() {
		int n=nextInt();
		block=(int) Math.sqrt(n);
		int m=nextInt();
		int[] co=nextIntArray(n);
		LinkedList<Integer>[] l=new LinkedList[n];
		for(int i=0;i<n;i++)
			l[i]=new LinkedList<>();
		for(int i=0;i<n-1;i++){
			int a=nextInt()-1;
			int b=nextInt()-1;
			l[a].add(b);
			l[b].add(a);
		}
		int[] dfs=new int[n+1];
		int[] st=new int[n+1];
		int[] et=new int[n+1];
		DFS(0,-1,dfs,st,et,l);
		Pair[] q=new Pair[m];
		for(int i=0;i<m;i++){
			int x=nextInt()-1;
			int k=nextInt();
			q[i]=new Pair(st[x],et[x],i,k);
		}
		Arrays.sort(q);
		int currL=0;
		int currR=-1;
		int[] cnt=new int[200001];
		int[] freq=new int[200001];
		int[] ans=new int[m];
		//System.out.println(cl+" "+cr);
		for(int i=0;i<m;i++){
			int L=q[i].x;
			int R=q[i].y;
			//System.out.println(cl+" "+cr);
			while(currL>L){
				currL--;
				cnt[co[dfs[currL]]]++;
				freq[cnt[co[dfs[currL]]]]++;
			}
			while(currR<R){
				currR++;
				cnt[co[dfs[currR]]]++;
				freq[cnt[co[dfs[currR]]]]++;
			}
			while(currL<L){
				freq[cnt[co[dfs[currL]]]]--;
				cnt[co[dfs[currL]]]--;
				currL++;
			}
			//System.out.println(cl+" "+cr);
			//System.out.println(cl+" "+cr);
			//System.out.println(cl+" "+cr);
			while(currR>R){
				freq[cnt[co[dfs[currR]]]]--;
				cnt[co[dfs[currR]]]--;
				currR--;
			}
			//System.out.println(cl+" "+cr);
			ans[q[i].ind]=freq[q[i].co];
		}
		for(int i=0;i<m;i++)
			pw.println(ans[i]);
	}
	static int j=0;
	private static void DFS(int cur,int prev,int[] dfs,int[] st,int[] et,LinkedList<Integer>[] l){
		st[cur]=j;
		dfs[j]=cur;
		Iterator<Integer> i=l[cur].listIterator();
		while(i.hasNext()){
			int x=i.next();
			if(x!=prev){
				j++;
				DFS(x,cur,dfs,st,et,l);
			}
		}
		et[cur]=j;
	}
	/*static class Suffix implements Comparable<Suffix>{
		int index;
		int[] rank=new int[2];
		@Override
		public int compareTo(Suffix arg0){
			return (this.rank[0]==arg0.rank[0])?(this.rank[1]<arg0.rank[1]?-1:1):(this.rank[0]<arg0.rank[0]?-1:1);
		}	
	}
	private static int[] buildSuffix(String s,int n){
		Suffix[] arr=new Suffix[n];
		for(int i=0;i<n;i++)
			arr[i]=new Suffix();
		for(int i=0;i<n;i++){
			arr[i].index=i;
			arr[i].rank[0]=s.charAt(i)-'a';
			arr[i].rank[1]=((i+1)<n)?(s.charAt(i+1)-'a'):-1;
		}
		Arrays.sort(arr);
		//for(int i=0;i<n;i++)
			//System.out.print(arr[i].index);
		int[] ind=new int[n];
		for(int k=4;k<2*n;k=k*2){
			int rank=0;
			int p_rank=arr[0].rank[0];
			arr[0].rank[0]=rank;
			ind[arr[0].index]=0;
			for(int i=1;i<n;i++){
				if (arr[i].rank[0] == p_rank && arr[i].rank[1] == arr[i-1].rank[1]) {
	                p_rank = arr[i].rank[0];
	                arr[i].rank[0] = rank;
	            }
	            else{
	                p_rank = arr[i].rank[0];
	                arr[i].rank[0] = ++rank;
	            }
	            ind[arr[i].index] = i;
	        }
			for(int i=0;i<n;i++){
				int n_index=arr[i].index + k/2;
				arr[i].rank[1]=(n_index<n)?arr[ind[n_index]].rank[0] : -1;
			}
			Arrays.sort(arr);
		}
		int[] suffixArr=new int[n];
		for(int i=0;i<n;i++)
			suffixArr[i]=arr[i].index;
		return suffixArr;
	}*/
	private static long pow(long a, long b, long c) {
		if (b == 0)
			return 1;
		long p = pow(a, b / 2, c);
		p = (p * p) % c;
		return (b % 2 == 0) ? p : (a * p) % c;
	}
	
	private static class Pair implements Comparable<Pair> {
		int x;
		int y;
		int ind;
		int co;
		public Pair(int a,int b,int i,int c) {
			x=a;y=b;ind=i;co=c;
		}
		@Override
		public int compareTo(Pair arg0) {
			return (x/block !=arg0.x/block)?(x/block-arg0.x/block):(y-arg0.y);
		}
	}

	private static long gcd(long a, long res1) {
		if (res1 == 0)
			return a;
		return gcd(res1, a % res1);
	}

	private static long max(long a, long b) {
		if (a > b)
			return a;
		return b;
	}

	private static long min(long a, long b) {
		if (a < b)
			return a;
		return b;
	}

	public static void main(String[] args) throws Exception {
		InputReader(System.in);
		pw = new PrintWriter(System.out);
		soln();
		pw.close();
	}

	public static void InputReader(InputStream stream1) {
		stream = stream1;
	}

	private static boolean isWhitespace(int c) {
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}

	private static boolean isEndOfLine(int c) {
		return c == '\n' || c == '\r' || c == -1;
	}

	private static int read() {
		if (numChars == -1)
			throw new InputMismatchException();
		if (curChar >= numChars) {
			curChar = 0;
			try {
				numChars = stream.read(buf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (numChars <= 0)
				return -1;
		}
		return buf[curChar++];
	}

	private static int nextInt() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		int res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	private static long nextLong() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		long res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	private static String nextToken() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isSpaceChar(c));
		return res.toString();
	}

	private static String nextLine() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isEndOfLine(c));
		return res.toString();
	}

	private static int[] nextIntArray(int n) {
		int[] arr = new int[n];
		for (int i = 0; i < n; i++) {
			arr[i] = nextInt();
		}
		return arr;
	}

	private static long[] nextLongArray(int n) {
		long[] arr = new long[n];
		for (int i = 0; i < n; i++) {
			arr[i] = nextLong();
		}
		return arr;
	}

	private static void pArray(int[] arr) {
		for (int i = 0; i < arr.length; i++) {
			System.out.print(arr[i] + " ");
		}
		System.out.println();
		return;
	}

	private static void pArray(long[] arr) {
		for (int i = 0; i < arr.length; i++) {
			System.out.print(arr[i] + " ");
		}
		System.out.println();
		return;
	}

	private static boolean isSpaceChar(int c) {
		if (filter != null)
			return filter.isSpaceChar(c);
		return isWhitespace(c);
	}

	private interface SpaceCharFilter {
		public boolean isSpaceChar(int ch);
	}
}