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;


public class Main {

    static int time;
    static ArrayList<Integer> adjList[];
    static int[] c, a, tin, tout;


    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int n = sc.nextInt();
        int m = sc.nextInt();
        Query.S = (int) (Math.sqrt(n) + 1);
        c = sc.nextIntArray(n);
        a = new int[n + 1];
        adjList = new ArrayList[n];
        for (int i = 0; i < n; i++)
            adjList[i] = new ArrayList<>();
        for (int i = 0; i < n - 1; i++) {
            int u = sc.nextInt() - 1;
            int v = sc.nextInt() - 1;
            adjList[u].add(v);
            adjList[v].add(u);
        }
        tin = new int[n];
        tout = new int[n];
        dfs(0, 0);
        Query[] queries = new Query[m];
        for (int i = 0; i < m; i++)
            queries[i] = new Query(sc.nextInt() - 1, sc.nextInt(), i);
        Arrays.sort(queries);
        int[] ans = new int[m];
        Counter counter = new Counter();
        int L = 0, R = 0;
        for (int i = 0; i < m; i++) {
            while (R < queries[i].r)
                counter.add(++R);
            while (L < queries[i].l)
                counter.remove(L++);
            while (L > queries[i].l)
                counter.add(--L);
            while (R > queries[i].r)
                counter.remove(R--);
            ans[queries[i].idx] = counter.getAns(queries[i].k);
        }
        for (int x : ans)
            out.println(x);
        out.flush();
        out.close();
    }

    static void dfs(int u, int p) {
        tin[u] = ++time;
        a[time] = c[u];
        for (int v : adjList[u])
            if (v != p) dfs(v, u);
        tout[u] = time;
    }

    static class Counter {
        static final int max = (int) (1e5 + 5);
        int[] cnt, occ;

        Counter() {
            cnt = new int[max];
            occ = new int[max];
        }

        void add(int x) {
            x = a[x];
            cnt[x]++;
            occ[cnt[x]]++;
        }

        void remove(int x) {
            x = a[x];
            occ[cnt[x]]--;
            cnt[x]--;
        }

        int getAns(int x) {
            return occ[x];
        }

        @Override
        public String toString() {
            return "Counter{" +
                    "cnt=" + Arrays.toString(cnt) +
                    ", occ=" + Arrays.toString(occ) +
                    '}';
        }
    }

    static class Query implements Comparable<Query> {
        static int S;
        int l, r, idx, leftBlock, k;

        public Query(int v, int k, int idx) {
            this.l = tin[v];
            this.r = tout[v];
            this.idx = idx;
            this.k = k;
            this.leftBlock = l / S;
        }

        @Override
        public int compareTo(Query o) {
            return leftBlock != o.leftBlock ? leftBlock - o.leftBlock : r - o.r;
        }

        @Override
        public String toString() {
            return "Query{" +
                    "l=" + l +
                    ", r=" + r +
                    ", idx=" + idx +
                    ", leftBlock=" + leftBlock +
                    ", k=" + k +
                    '}';
        }
    }


    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream system) {
            br = new BufferedReader(new InputStreamReader(system));
        }

        public Scanner(String file) throws Exception {
            br = new BufferedReader(new FileReader(file));
        }


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

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

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

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

        public char nextChar() throws IOException {
            return next().charAt(0);
        }

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

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


        public int[] nextIntArray(int n) throws IOException {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        public long[] nextLongArray(int n) throws IOException {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }


        public Integer[] nextIntegerArray(int n) throws IOException {
            Integer[] a = new Integer[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        public double[] nextDoubleArray(int n) throws IOException {
            double[] ans = new double[n];
            for (int i = 0; i < n; i++)
                ans[i] = nextDouble();
            return ans;
        }

        public short nextShort() throws IOException {
            return Short.parseShort(next());
        }

    }
}