#P1677E. Tokitsukaze and Beautiful Subsegments
Tokitsukaze and Beautiful Subsegments
Description
Tokitsukaze has a permutation $p$ of length $n$.
Let's call a segment $[l,r]$ beautiful if there exist $i$ and $j$ satisfying $p_i \cdot p_j = \max\{p_l, p_{l+1}, \ldots, p_r \}$, where $l \leq i < j \leq r$.
Now Tokitsukaze has $q$ queries, in the $i$-th query she wants to know how many beautiful subsegments $[x,y]$ there are in the segment $[l_i,r_i]$ (i. e. $l_i \leq x \leq y \leq r_i$).
The first line contains two integers $n$ and $q$ ($1\leq n \leq 2 \cdot 10^5$; $1 \leq q \leq 10^6$) — the length of permutation $p$ and the number of queries.
The second line contains $n$ distinct integers $p_1, p_2, \ldots, p_n$ ($1 \leq p_i \leq n$) — the permutation $p$.
Each of the next $q$ lines contains two integers $l_i$ and $r_i$ ($1 \leq l_i \leq r_i \leq n$) — the segment $[l_i,r_i]$ of this query.
For each query, print one integer — the numbers of beautiful subsegments in the segment $[l_i,r_i]$.
Input
The first line contains two integers $n$ and $q$ ($1\leq n \leq 2 \cdot 10^5$; $1 \leq q \leq 10^6$) — the length of permutation $p$ and the number of queries.
The second line contains $n$ distinct integers $p_1, p_2, \ldots, p_n$ ($1 \leq p_i \leq n$) — the permutation $p$.
Each of the next $q$ lines contains two integers $l_i$ and $r_i$ ($1 \leq l_i \leq r_i \leq n$) — the segment $[l_i,r_i]$ of this query.
Output
For each query, print one integer — the numbers of beautiful subsegments in the segment $[l_i,r_i]$.
Samples
8 3
1 3 5 2 4 7 6 8
1 3
1 1
1 8
2
0
10
10 10
6 1 3 2 5 8 4 10 7 9
1 8
1 10
1 2
1 4
2 4
5 8
4 10
4 7
8 10
5 9
17
25
1
5
2
0
4
1
0
0
Note
In the first example, for the first query, there are $2$ beautiful subsegments — $[1,2]$ and $[1,3]$.