Let a_1, …, a_n be an array of n positive integers. In one operation, you can choose an index i such that a_i = i, and remove a_i from the array (after the removal, the remaining parts are concatenated).

The weight of a is defined as the maximum number of elements you can remove.

You must answer q independent queries (x, y): after replacing the x first elements of a and the y last elements of a by n+1 (making them impossible to remove), what would be the weight of a?

Input

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

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

The i-th of the next q lines contains two integers x and y (x, y ≥ 0 and x+y < n).

Output

Print q lines, i-th line should contain a single integer — the answer to the i-th query.

Examples

Input


13 5
2 2 3 9 5 4 6 5 7 8 3 11 13
3 1
0 0
2 4
5 0
0 12


Output


5
11
6
1
0


Input


5 2
1 4 1 2 4
0 0
1 0


Output


2
0

Note

Explanation of the first query:

After making first x = 3 and last y = 1 elements impossible to remove, a becomes [×, ×, ×, 9, 5, 4, 6, 5, 7, 8, 3, 11, ×] (we represent 14 as × for clarity).

Here is a strategy that removes 5 elements (the element removed is colored in red):

  * [×, ×, ×, 9, \color{red}{5}, 4, 6, 5, 7, 8, 3, 11, ×] 
  * [×, ×, ×, 9, 4, 6, 5, 7, 8, 3, \color{red}{11}, ×] 
  * [×, ×, ×, 9, 4, \color{red}{6}, 5, 7, 8, 3, ×] 
  * [×, ×, ×, 9, 4, 5, 7, \color{red}{8}, 3, ×] 
  * [×, ×, ×, 9, 4, 5, \color{red}{7}, 3, ×] 
  * [×, ×, ×, 9, 4, 5, 3, ×] (final state) 



It is impossible to remove more than 5 elements, hence the weight is 5.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "", 1 << 27);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastReader in = new FastReader(inputStream);
            PrintWriter out = new PrintWriter(outputStream);
            CFixedPointRemoval solver = new CFixedPointRemoval();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class CFixedPointRemoval {
        bit b;

        public void solve(int testNumber, FastReader s, PrintWriter w) {
            int n = s.nextInt(), q = s.nextInt();
            b = new bit(n + 10);
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = s.nextInt() - 1;
            ArrayList<pair<Integer, Integer>>[] queries = new ArrayList[n];
            for (int i = 0; i < n; i++) queries[i] = new ArrayList<>();
            for (int i = 0; i < q; i++) {
                int l = s.nextInt();
                queries[n - s.nextInt() - 1].add(new pair<>(l, i));
            }
            int[] res = new int[q];
            for (int i = 0; i < n; i++) {
                int dif = i - a[i];
                int best = dif < 0 ? -1 : get(0, i, dif);
                b.modify(0, 1);
                b.modify(best + 1, -1);
                for (pair<Integer, Integer> p : queries[i])
                    res[p.y] = b.query(p.x);
            }
            for (int i = 0; i < q; i++) w.println(res[i]);
        }

        int get(int l, int r, int dif) {
            int mid;
            while (l <= r) {
                mid = l + r >> 1;
                if (b.query(mid) >= dif) l = mid + 1;
                else r = mid - 1;
            }
            return --l;
        }

    }

    static class bit {
        public int n;
        public int[] t;

        public bit(int n) {
            t = new int[n];
            this.n = n;
        }

        public bit(int[] a, int n) {
            t = new int[n];
            this.n = n;
            for (int i = 0; i < n; i++) {
                modify(i, a[i]);
            }
        }

        public void modify(int ind, int val) {
            for (; ind < n; ind |= ++ind) t[ind] += val;
        }

        public int query(int ind) {
            int sum = 0;
            for (; ind >= 0; ind &= ++ind, --ind) sum += t[ind];
            return sum;
        }

    }

    static class FastReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private FastReader.SpaceCharFilter filter;

        public FastReader(InputStream stream) {
            this.stream = stream;
        }

        public 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++];
        }

        public 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;
        }

        public boolean isSpaceChar(int c) {

            if (filter != null)
                return filter.isSpaceChar(c);

            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

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

        }

    }

    static class pair<U extends Comparable<U>, V extends Comparable<V>> implements Comparable<pair<U, V>> {
        public U x;
        public V y;

        public pair(U x, V y) {
            this.x = x;
            this.y = y;
        }

        public int compareTo(pair<U, V> other) {
            int cmp = x.compareTo(other.x);
            return cmp == 0 ? y.compareTo(other.y) : cmp;
        }

        public String toString() {
            return x.toString() + " " + y.toString();
        }

        public boolean equals(Object obj) {
            if (this.getClass() != obj.getClass()) return false;
            pair<U, V> other = (pair<U, V>) obj;
            return x.equals(other.x) && y.equals(other.y);
        }

        public int hashCode() {
            return 31 * x.hashCode() + y.hashCode();
        }

    }
}

