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.Vector;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author xwchen
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int q = in.nextInt();
            int[] a = in.nextIntArray1(n);
            Vector<Integer>[] endHere = new Vector[n + 1];
            int[] leftPoint = new int[q + 1];
            long[] ans = new long[q + 1];
            for (int i = 1; i <= n; ++i) {
                endHere[i] = new Vector<>();
            }
            for (int i = 0; i < q; ++i) {
                int l = in.nextInt() + 1;
                int r = n - in.nextInt();
                endHere[r].add(i);
                leftPoint[i] = l;
            }
            BinaryIndexedTree bit = new BinaryIndexedTree(n);
            for (int r = 1; r <= n; ++r) {
                a[r] = r - a[r];
                if (a[r] >= 0) {
                    int left = 1;
                    int right = r;
                    int pv = 0;
                    while (left <= right) {
                        int mid = (left + right) / 2;
                        if (bit.sum(mid) >= a[r]) {
                            left = mid + 1;
                            pv = mid;
                        } else {
                            right = mid - 1;
                        }
                    }
                    bit.update(1, 1);
                    bit.update(pv + 1, -1);
                }
                for (int j : endHere[r]) {
                    ans[j] = bit.sum(leftPoint[j]);
                }
            }
            for (int i = 0; i < q; ++i) {
                out.println(ans[i]);
            }

        }

    }

    static class InputReader {
        private BufferedReader reader;
        private StringTokenizer tokenizer = new StringTokenizer("");

        public InputReader(InputStream inputStream) {
            this.reader = new BufferedReader(
                    new InputStreamReader(inputStream));
        }

        public String next() {
            while (!tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return tokenizer.nextToken();
        }

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

        public int[] nextIntArray1(int n) {
            int[] a = new int[n + 1];
            for (int i = 1; i <= n; i++)
                a[i] = nextInt();
            return a;
        }

    }

    static class BinaryIndexedTree {
        int n;
        public long[] bit;

        public BinaryIndexedTree(int n) {
            this.n = n;
            bit = new long[n + 1];
        }

        public void update(int i, int add) {
            while (i > 0 && i <= n) {
                bit[i] += add;
                i = i + (i & (-i));
            }
        }

        public long sum(int i) {
            long ans = 0;
            while (i > 0) {
                ans += bit[i];
                i = i - (i & (-i));
            }
            return ans;
        }

    }
}

