Baby Ehab has a piece of Cut and Stick with an array a of length n written on it. He plans to grab a pair of scissors and do the following to it:

  * pick a range (l, r) and cut out every element a_l, a_{l + 1}, ..., a_r in this range; 
  * stick some of the elements together in the same order they were in the array; 
  * end up with multiple pieces, where every piece contains some of the elements and every element belongs to some piece. 



More formally, he partitions the sequence a_l, a_{l + 1}, ..., a_r into subsequences. He thinks a partitioning is beautiful if for every piece (subsequence) it holds that, if it has length x, then no value occurs strictly more than ⌈ x/2 ⌉ times in it.

He didn't pick a range yet, so he's wondering: for q ranges (l, r), what is the minimum number of pieces he needs to partition the elements a_l, a_{l + 1}, ..., a_r into so that the partitioning is beautiful.

A sequence b is a subsequence of an array a if b can be obtained from a by deleting some (possibly zero) elements. Note that it does not have to be contiguous.

Input

The first line contains two integers n and q (1 ≤ n,q ≤ 3 ⋅ 10^5) — the length of the array a and the number of queries.

The second line contains n integers a_1, a_2, ..., a_{n} (1 ≤ a_i ≤ n) — the elements of the array a.

Each of the next q lines contains two integers l and r (1 ≤ l ≤ r ≤ n) — the range of this query.

Output

For each query, print the minimum number of subsequences you need to partition this range into so that the partitioning is beautiful. We can prove such partitioning always exists.

Example

Input


6 2
1 3 2 3 3 2
1 6
2 5


Output


1
2

Note

In the first query, you can just put the whole array in one subsequence, since its length is 6, and no value occurs more than 3 times in it.

In the second query, the elements of the query range are [3,2,3,3]. You can't put them all in one subsequence, since its length is 4, and 3 occurs more than 2 times. However, you can partition it into two subsequences: [3] and [2,3,3].


import java.io.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.util.Arrays;
import java.util.Random;

public final class D {

    public static void main(String[] args) throws IOException {
        final FastReader fs = new FastReader();
        final StringBuilder sb = new StringBuilder();
        final int n = fs.nextInt();
        final int q = fs.nextInt();
        final int[] arr = new int[n];
        final int[][] edges = new int[n][2];
        for (int i = 0; i < n; i++) {
            arr[i] = fs.nextInt();
            edges[i] = new int[] { arr[i], i };
        }
        final int[][] g = packG(edges, n + 1);
        final Random rand = new Random();
        for (int i = 0; i < q; i++) {
            final int l = fs.nextInt() - 1;
            final int r = fs.nextInt() - 1;
            final int len = r - l + 1;
            int max = 0;
            for (int j = 0; j < 40; j++) {
                final int curr = arr[l + rand.nextInt(len)];
                final int[] list = g[curr];
                final int ll = lowerBound(list, l);
                final int rr = upperBound(list, r);
                max = Math.max(max, rr - ll + 1);
            }
            sb.append(Math.max(1, (2 * max) - len));
            sb.append('\n');
        }
        System.out.println(sb);
    }

    private static int[][] packG(int[][] edges, int n) {
        final int[][] g = new int[n][];
        final int[] size = new int[n];
        final int[] idx = new int[n];
        for (int[] edge : edges) {
            ++size[edge[0]];
        }
        for (int i = 0; i < n; i++) {
            g[i] = new int[size[i]];
        }
        for (int[] edge : edges) {
            g[edge[0]][idx[edge[0]]++] = edge[1];
        }
        return g;
    }

    private static int lowerBound(int[] l, int tar) {
        int lo = 0, hi = l.length;
        while (lo < hi) {
            final int mid = lo + hi >>> 1;
            if (l[mid] < tar) {
                lo = mid + 1;
            } else {
                hi = mid;
            }
        }
        return lo;
    }

    private static int upperBound(int[] l, int tar) {
        int lo = 0, hi = l.length - 1;
        while (lo < hi) {
            final int mid = lo + hi + 1 >>> 1;
            if (l[mid] > tar) {
                hi = mid - 1;
            } else {
                lo = mid;
            }
        }
        return lo;
    }

    static final class Utils {
        private static class Shuffler {
            private static void shuffle(int[] x) {
                final Random r = new Random();

                for (int i = 0; i <= x.length - 2; i++) {
                    final int j = i + r.nextInt(x.length - i);
                    swap(x, i, j);
                }
            }

            private static void shuffle(long[] x) {
                final Random r = new Random();

                for (int i = 0; i <= x.length - 2; i++) {
                    final int j = i + r.nextInt(x.length - i);
                    swap(x, i, j);
                }
            }

            private static void swap(int[] x, int i, int j) {
                final int t = x[i];
                x[i] = x[j];
                x[j] = t;
            }

            private static void swap(long[] x, int i, int j) {
                final long t = x[i];
                x[i] = x[j];
                x[j] = t;
            }
        }

        public static void shuffleSort(int[] arr) {
            Shuffler.shuffle(arr);
            Arrays.sort(arr);
        }

        public static void shuffleSort(long[] arr) {
            Shuffler.shuffle(arr);
            Arrays.sort(arr);
        }

        private Utils() {}
    }

    static class FastReader {
        private static final int BUFFER_SIZE = 1 << 16;
        private final DataInputStream din;
        private final byte[] buffer;
        private int bufferPointer, bytesRead;

        FastReader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        FastReader(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException {
            final byte[] buf = new byte[1024]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n') {
                    break;
                }
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextSign() throws IOException {
            byte c = read();
            while ('+' != c && '-' != c) {
                c = read();
            }
            return '+' == c ? 0 : 1;
        }

        private static boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }

        private int skip() throws IOException {
            int b;
            //noinspection StatementWithEmptyBody
            while ((b = read()) != -1 && isSpaceChar(b)) {}
            return b;
        }

        public char nc() throws IOException {
            return (char) skip();
        }

        public String next() throws IOException {
            int b = skip();
            final StringBuilder sb = new StringBuilder();
            while (!isSpaceChar(b)) { // when nextLine, (isSpaceChar(b) && b != ' ')
                sb.appendCodePoint(b);
                b = read();
            }
            return sb.toString();
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ') {
                c = read();
            }
            final boolean neg = c == '-';
            if (neg) { c = read(); }
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (neg) { return -ret; }
            return ret;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ') { c = read(); }
            final boolean neg = c == '-';
            if (neg) { c = read(); }
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg) { return -ret; }
            return ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ') { c = read(); }
            final boolean neg = c == '-';
            if (neg) { c = read(); }

            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');

            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg) { return -ret; }
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1) { buffer[0] = -1; }
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead) { fillBuffer(); }
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            din.close();
        }
    }
}
