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 D {
    static int V, SQRT, Q;
    static int [] col, idx, sz;
    static ArrayList<Integer> order, tree [];

    static void dfs (int node, int parent) {
        sz[node] = 1;
        order.add(node);
        idx[node] = order.size() - 1;

        for (int child : tree[node]) {
            if (child != parent) {
                dfs(child, node);
                sz[node] += sz[child];
            }
        }
    }
    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        V = sc.nextInt();
        Q = sc.nextInt();

        col = new int[V];
        idx = new int[V];
        sz = new int[V];
        order = new ArrayList<>(V);
        SQRT = (int) Math.sqrt(V);
        tree = new ArrayList[V];

        for (int i = 0; i < V; i++) {
            tree[i] = new ArrayList<>();
            col[i] = sc.nextInt();
        }

        for (int i = 0; i < V - 1; i++) {
            int u = sc.nextInt() - 1;
            int v = sc.nextInt() - 1;
            tree[u].add(v);
            tree[v].add(u);
        }

        dfs (0, - 1);

        Query queries [] = new Query[Q];
        for (int i = 0; i < Q; i++) {
            int v = sc.nextInt() - 1;
            int l = idx[v];
            int r = l + sz[v] - 1;
            queries[i] = new Query(l, r, i, sc.nextInt());
        }
        Arrays.sort(queries);

        int cnt [] = new int[(int)1e5 + 10];
        int occ [] = new int[(int)1e5 + 10];
        int res [] = new int[Q];
        int L = 0, R = - 1;

        for (int i = 0; i < Q; i++) {
            int curL = queries[i].l;
            int curR = queries[i].r;

            while (L > curL) {
                occ[++cnt[col[order.get(--L)]]]++;
            }
            while (R < curR) {
                occ[++cnt[col[order.get(++R)]]]++;
            }
            while (L < curL) {
                occ[cnt[col[order.get(L++)]]--]--;
            }
            while (R > curR) {
                occ[cnt[col[order.get(R--)]]--]--;
            }

            res[queries[i].idx] = occ[queries[i].minOcc];
        }

        PrintWriter out = new PrintWriter(System.out);
        for (int i : res) {
            out.println(i);
        }
        out.close();
    }

    static class Query implements Comparable<Query> {
        int l, r, idx, minOcc;
        Query (int ll, int rr, int ii, int mm) {
            l = ll;
            r = rr;
            idx = ii;
            minOcc = mm;
        }

        @Override
        public int compareTo(Query query) {
            int sqF = l / SQRT , sqS = query.l / SQRT;
            return sqF == sqS ? r - query.r : sqF - sqS;
        }
    }














    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }
        public Scanner (FileReader f) { br = new BufferedReader(f);}

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

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

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

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public double nextDouble() throws IOException {
            String x = next();
            StringBuilder sb = new StringBuilder("0");
            double res = 0, f = 1;
            boolean dec = false, neg = false;
            int start = 0;
            if (x.charAt(0) == '-') {
                neg = true;
                start++;
            }
            for (int i = start; i < x.length(); i++)
                if (x.charAt(i) == '.') {
                    res = Long.parseLong(sb.toString());
                    sb = new StringBuilder("0");
                    dec = true;
                } else {
                    sb.append(x.charAt(i));
                    if (dec)
                        f *= 10;
                }
            res += Long.parseLong(sb.toString()) / f;
            return res * (neg ? -1 : 1);
        }

        public boolean ready() throws IOException {
            return br.ready();
        }

    }
}