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C. Fixed Point Removal

time limit per test

4 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputLet $$$a_1, \ldots, a_n$$$ 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 $$$q$$$ ($$$1 \le n, q \le 3 \cdot 10^5$$$) — 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.

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 $$$[\times, \times, \times, 9, 5, 4, 6, 5, 7, 8, 3, 11, \times]$$$ (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 $$$5$$$.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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