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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Comparator;
import java.util.Random;
import java.util.StringTokenizer;

public final class E {

    public static class BIT {
        private final int[] bit;

        public BIT(int n) {
            bit = new int[n + 1];
        }

        public void add(int i, int val) {
            i++;
            while (i < bit.length) {
                bit[i] += val;
                i += lsb(i);
            }
        }

        private void rangeUpdate(int l, int r, int val) {
            add(l, val);
            add(r + 1, -val);
        }

        public int query(int i) {
            i++;
            int ans = 0;
            while (i > 0) {
                ans += bit[i];
                i -= lsb(i);
            }
            return ans;
        }

        private static int lsb(int i) {
            return i & -i;  // zeroes all the bits except the least significant one
        }
    }

    public static void main(String[] args) {
        final FastScanner fs = new FastScanner();
        final int n = fs.nextInt();
        final int nQ = fs.nextInt();
        final int[] a = fs.nextIntArray(n);
        for (int i = 0; i < n; i++) {
            a[i]--;
        }
        final int[][] queries = new int[nQ][3];
        final int[][] unsorted = new int[nQ][3];
        for (int qq = 0; qq < nQ; qq++) {
            unsorted[qq] = queries[qq] = new int[] { fs.nextInt(), n - 1 - fs.nextInt(), 0 };
        }
        Arrays.sort(queries, Comparator.comparingInt(v -> v[1]));
        final BIT bit = new BIT(n);
        int queryIndex = 0;
        for (int r = 0; r < n; r++) {
            if (a[r] <= r && r - bit.query(0) <= a[r]) {
                int lo = 0, hi = r;
                while (lo < hi) {
                    final int mid = lo + hi + 1 >>> 1;
                    final int res = bit.query(mid);
                    if (a[r] >= r - res && a[r] <= r) {
                        lo = mid;
                    } else {
                        hi = mid - 1;
                    }
                }
                bit.rangeUpdate(0, lo, 1);
            }
            while (queryIndex < nQ && queries[queryIndex][1] == r) {
                final int[] query = queries[queryIndex++];
                query[2] = bit.query(query[0]);
            }
        }
        final PrintWriter pw = new PrintWriter(System.out);
        for (int[] qq : unsorted) {
            pw.println(qq[2]);
        }
        pw.flush();
    }

    static final class Util {
        public static void shuffleSort(int[] x) {
            shuffle(x);
            Arrays.sort(x);
        }

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

        public 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);
            }
        }

        public 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);
            }
        }

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

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

        private Util() {}
    }

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

        private String next() {
            while (!st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    //noinspection CallToPrintStackTrace
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

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

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