Fixed Point Removal

Description:

Input:

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

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

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

Output:

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

Sample 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

Sample Output:

5
11
6
1
0

Sample Input:

5 2
1 4 1 2 4
0 0
1 0

Sample Output:

2
0

Note:

Explanation of the first query:

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

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

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

It is impossible to remove more than $$$5$$$ elements, hence the weight is $$$5$$$.