Tokitsukaze and Beautiful Subsegments

题目描述

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. $l_i \leq x \leq y \leq r_i$ ).

输入输出格式

输入格式

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.

输出格式

For each query, print one integer — the numbers of beautiful subsegments in the segment $[l_i,r_i]$ .

输入输出样例

输入样例 #1

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

输出样例 #1

2
0
10

输入样例 #2

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

输出样例 #2

17
25
1
5
2
0
4
1
0
0

说明

In the first example, for the first query, there are $2$ beautiful subsegments — $[1,2]$ and $[1,3]$ .