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.util.*;
 
public class Main {
    static int []BIT;
 
    static void add(int x,int v) {
        for (int i = x+1; i > 0; i -= i & (-i)) {
            BIT[i]+=v;
        }
    }
 
    static int get(int x) {
        int s = 0;
        for (int i = x+1; i < BIT.length; i+= i & (-i)) {
            s += BIT[i];
        }
        return s;
    }
 
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        BIT = new int[n + 20];
        int q = scanner.nextInt();
        int []N = new int[n];
        for (int i = 0; i < n; i++) {
            N[i] = (i + 1) - scanner.nextInt();
        }
        int [][]Q = new int[q][3];
        HashMap<Integer, List<Integer>> QueryMap = new HashMap<>();
        for (int i = 0; i < q; i++) {
            Q[i][0] = scanner.nextInt();
            Q[i][1] = n - scanner.nextInt() - 1;
            Q[i][2] = 0;
            if (!QueryMap.containsKey(Q[i][1])) {
                QueryMap.put(Q[i][1], new LinkedList<Integer>());
            }
            QueryMap.get(Q[i][1]).add(i);
        }
        int ss = 0;
        for (int i = 0; i < n; i++) {
            if (N[i] == 0) {
                add(i, 1);
                //System.out.println(i);
            } else if (N[i] >= 0 && get(0) >= N[i]) {
                int lo = 0;
                int hi = i;
                while (lo < hi - 1) {
                    int m = (lo + hi) / 2;
                    int v = get(m);
                    if (v >= N[i]) {
                        lo = m;
                    } else {
                        hi = m;
                    }
                }
                add(lo, 1);
                //System.out.println(lo);
            }
            if (ss >= N[i] && N[i] >= 0) ss++;
            //System.out.println(ss + "(" + get(0) + ")" + " " + i + " " + N[i]);
            if (QueryMap.containsKey(i)) {
                for (Integer queryIndex : QueryMap.get(i)) {
                    Q[queryIndex][2] = get(Q[queryIndex][0]);
                }
            }
        }
 
        for (int i = 0; i < q; i++) {
            System.out.println(Q[i][2]);
        }
 
    }
}