CF1404C.Fixed Point Removal

Let $a_1, \ldots, a_n$ 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 $a$?

设 $a_1, \ldots, a_n$ 是一个由 $n$ 个正整数组成的数组。一次操作中，你可以选择一个下标 $i$，满足 $a_i = i$，然后将 $a_i$ 从数组中删除（删除后，剩余部分会拼接在一起）。

数组 $a$ 的权重定义为：你能删除的元素的最大数量。

你需要回答 $q$ 个独立的查询 $(x, y)$：将 $a$ 的前 $x$ 个元素和后 $y$ 个元素均替换为 $n+1$（使其无法被删除）后，$a$ 的权重是多少？

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 $x+y \lt n$).

第一行包含两个整数 $n$ 和 $q$（$1 \le n, q \le 3 \cdot 10^5$）—— 分别表示数组的长度和查询次数。

第二行包含 $n$ 个整数 $a_1$, $a_2$, ..., $a_n$（$1 \leq a_i \leq n$）—— 数组的元素。

接下来的 $q$ 行中，第 $i$ 行包含两个整数 $x$ 和 $y$（$x, y \ge 0$ 且 $x+y \lt n$）。

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

输出 $q$ 行，第 $i$ 行应包含一个整数——即第 $i$ 个查询的答案。

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 $5$.

第一次查询的解释：

在使最前面 $x = 3$ 个元素和最后面 $y = 1$ 个元素不可删除之后，数组 $a$ 变为 $[\times, \times, \times, 9, 5, 4, 6, 5, 7, 8, 3, 11, \times]$（为清晰起见，我们用 $\times$ 表示不可删除的元素）。

以下是一种可删除 $5$ 个元素的策略（被删除的元素以红色标出）：

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

无法删除超过 $5$ 个元素，因此该查询的权值为 $5$。