Description

Input

The first line of input contains two integers, $n$ and $q$ ($1 \leq n, q \leq 200\,000$)  — the length of the array $a$ and the number of queries.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \leq a_i \leq 10^9$)  — the values of the array $a$.

Each of the next $q$ lines contains the description of a query. Each line contains two integers $l$ and $r$ ($1 \leq l \leq r \leq n$)  — the query is about the subarray $a_l, a_{l+1}, \dots, a_r$.

Output

For each of the $q$ queries, print a line containing the length of the longest almost-increasing subsequence of the subarray $a_l, a_{l+1}, \dots, a_r$.

9 8
1 2 4 3 3 5 6 2 1
1 3
1 4
2 5
6 6
3 7
7 8
1 8
8 8

3
4
3
1
4
2
7
1

Note

In the first query, the subarray is $a_1, a_2, a_3 = [1,2,4]$. The whole subarray is almost-increasing, so the answer is $3$.

In the second query, the subarray is $a_1, a_2, a_3,a_4 = [1,2,4,3]$. The whole subarray is a almost-increasing, because there are no three consecutive elements such that $x \geq y \geq z$. So the answer is $4$.

In the third query, the subarray is $a_2, a_3, a_4, a_5 = [2, 4, 3, 3]$. The whole subarray is not almost-increasing, because the last three elements satisfy $4 \geq 3 \geq 3$. An almost-increasing subsequence of length $3$ can be found (for example taking $a_2,a_3,a_5 = [2,4,3]$ ). So the answer is $3$.