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.
/**
 * Accomplished using the EduTools plugin by JetBrains https://plugins.jetbrains.com/plugin/10081-edutools
 */

import java.io.*;
import java.util.*;

public class Main {
   public static void main(String[] args) throws IOException {
      BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
      BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));

      String[] line = br.readLine().split(" ");
      int n = Integer.parseInt(line[0]), q = Integer.parseInt(line[1]);
      int[] a = new int[n];
      line = br.readLine().split(" ");
      for (int i = 0; i < n; ++i) {
          a[i] = i - Integer.parseInt(line[i]) + 1;
      }
      int[][] queries = new int[q][2];
      for (int i = 0; i < q; ++i) {
          line = br.readLine().split(" ");
          for (int j = 0; j < 2; ++j) {
             queries[i][j] = Integer.parseInt(line[j]);
          }
      }

      int[] ans = new int[q];
      List<Integer>[] endings = new List[n];
      for (int i = 0; i < n; ++i) {
          endings[i] = new ArrayList<>();
      }
      for (int i = 0; i < q; ++i) {
          endings[n - queries[i][1] - 1].add(i);
      }

      int[] fenwickTree = new int[n + 1];
      int prefInd = 0, log2 = 0;
      for (int i = 1; i < n; i <<= 1) {
          ++log2;
      }

      for (int r = 0; r < n; ++r) {
            int target = a[r];
            if (target >= 0) {
                int pos = 0, cur = prefInd;
                for (int jump = 1 << log2; jump >= 1; jump >>= 1) {
                    if (pos + jump <= r + 1 && cur - fenwickTree[pos + jump] >= target) {
                        pos += jump;
                        cur -= fenwickTree[pos];
                    }
                }

                ++prefInd;
                for (int i = pos + 1; i <= n; i += i & -i) {
                    ++fenwickTree[i];
                }
            }

            for (int query: endings[r]) {
                ans[query] = prefInd;
                for (int i = queries[query][0] + 1; i > 0; i -= i & -i) {
                    ans[query] -= fenwickTree[i];
                }
            }
      }

      for (int answer: ans) {
          bw.write(Integer.toString(answer));
          bw.newLine();
      }

      br.close();
      bw.close();
   }
}