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.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;

/**
 * Created by mostafa on 10/31/17.
 */
public class TreeQueries {
    static class Q implements Comparable<Q>{
        int l, r, o, i;
        Q(int a, int b, int c, int idx) {
            l = a; r = b;
            o = c; i = idx;
        }
        @Override
        public int compareTo(Q q) {
            int b1 = l / k, b2 = q.l / k;
            if(b1 == b2)
                return r - q.r;
            return b1 - b2;
        }
    }

    static ArrayList<Integer>[] adj;
    static int N;
    static int[] tin;
    static int[] size;
    static int dfs_num;
    static int k;
    static void dfs(int u, int p) {
        tin[u] = dfs_num++;
        size[u] = 1;
        for(int v: adj[u])
            if(v != p) {
                dfs(v, u);
                size[u] += size[v];
            }
    }
    static int[] c;
    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner();
        N = sc.nextInt();
        int m = sc.nextInt();

        k = (int) Math.sqrt(N);
        c = new int[N];
        adj = new ArrayList[N];

        for(int i = 0; i < N; i++) {
            adj[i] = new ArrayList<>();
            c[i] = sc.nextInt();
        }

        for(int i = 0; i < N - 1; i++) {
            int u = sc.nextInt() - 1, v = sc.nextInt() - 1;
            adj[u].add(v); adj[v].add(u);
        }
        int max = (int) 1e5 + 1;
        occ = new int[max];
        tin = new int[N]; size = new int[N]; ctin = new int[N]; ans = new int[max];
        int[] sol = new int[m];
        dfs(0, -1);
        for(int i = 0; i < N; i++)
            ctin[tin[i]] = c[i];

        Q[] q = new Q[m];
        for(int i = 0; i < m; i++) {
            int v = sc.nextInt() - 1, k = sc.nextInt();
            int l = tin[v], r = tin[v] + size[v] - 1;
            q[i] = new Q(l, r, k, i);
        }

        Arrays.sort(q);
        int l = 0, r = 0;

        for(int i = 0; i < m; i++) {
            while(l < q[i].l)
                rem(l++);
            while(l > q[i].l)
                add(--l);
            while(r <= q[i].r)
                add(r++);
            while(r > q[i].r + 1)
                rem(--r);
            sol[q[i].i] = ans[q[i].o];
        }
        PrintWriter out = new PrintWriter(System.out);
        for(int i = 0; i < m; i++)
            out.println(sol[i]);
        out.flush();
        out.close();
    }
    static int[] occ, ans;
    static void add(int i) {
        occ[ctin[i]]++;
        if(occ[ctin[i]] >= 0) {
            ans[occ[ctin[i]]]++;
        }
    }

    static void rem(int i) {
        if(occ[ctin[i]] >= 0) {
            ans[occ[ctin[i]]]--;
        }
        occ[ctin[i]]--;
    }

    static int[] ctin;

    static class Scanner {
        BufferedReader br;
        StringTokenizer st;
        Scanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        Scanner(String f) throws FileNotFoundException {
            br = new BufferedReader(new FileReader(f));
        }

        String next() throws IOException {
            while(st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

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

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

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